[{"data":1,"prerenderedAt":5029},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-kegelstumpf":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-kegelstumpf":5016},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":555,"category":247,"checks":4799,"conditions":4832,"conditionsHtml":4833,"deprecated":4834,"description":4792,"extension":4835,"figure":4836,"figureCaption":4837,"figureHtml":4977,"formulaId":4978,"latex":4979,"latexHtml":4980,"level":4981,"meta":4982,"navigation":4926,"path":4983,"redirectFrom":4984,"related":4985,"seo":4990,"stem":4991,"subject":582,"summary":4992,"tags":4993,"variables":4998,"__hash__":5015},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-kegelstumpf.md","Volumen eines Kegelstumpfs",[550,551,552,553,554],"Volumen Kegelstumpf","Kegelstumpf Volumen berechnen","Kegelstumpf Formel","V = πh\u002F3 (R² + Rr + r²)","Volumen Eimer",{"type":556,"value":557,"toc":4791},"minimark",[558,563,652,655,1228,1232,1579,1883,1886,2675,2971,2975,3179,3742,3877,4350,4395,4399],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,571,572,619,620,651],"p",{},"Ein ",[568,569,570],"strong",{},"Kegelstumpf"," entsteht, wenn man von einem Kegel die Spitze parallel zur Grundfläche abschneidet. Er hat zwei parallele Kreisflächen mit verschiedenen Radien: dem größeren Radius ",[573,574,577,599],"span",{"className":575},[576],"katex",[573,578,581],{"className":579},[580],"katex-mathml",[582,583,585],"math",{"xmlns":584},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[586,587,588,595],"semantics",{},[589,590,591],"mrow",{},[592,593,594],"mi",{},"R",[596,597,594],"annotation",{"encoding":598},"application\u002Fx-tex",[573,600,604],{"className":601,"ariaHidden":603},[602],"katex-html","true",[573,605,608,613],{"className":606},[607],"base",[573,609],{"className":610,"style":612},[611],"strut","height:0.6833em;",[573,614,594],{"className":615,"style":618},[616,617],"mord","mathnormal","margin-right:0.0077em;"," und dem kleineren Radius ",[573,621,623,637],{"className":622},[576],[573,624,626],{"className":625},[580],[582,627,628],{"xmlns":584},[586,629,630,635],{},[589,631,632],{},[592,633,634],{},"r",[596,636,634],{"encoding":598},[573,638,640],{"className":639,"ariaHidden":603},[602],[573,641,643,647],{"className":642},[607],[573,644],{"className":645,"style":646},[611],"height:0.4306em;",[573,648,634],{"className":649,"style":650},[616,617],"margin-right:0.0278em;",". Typische Beispiele sind Eimer, Blumentöpfe, Trinkbecher und Lampenschirme.",[564,653,654],{},"Die Formel enthält zwei Sonderfälle:",[656,657,658,924],"ul",{},[659,660,661,720,721,923],"li",{},[573,662,664,686],{"className":663},[576],[573,665,667],{"className":666},[580],[582,668,669],{"xmlns":584},[586,670,671,683],{},[589,672,673,675,679],{},[592,674,634],{},[676,677,678],"mo",{},"=",[680,681,682],"mn",{},"0",[596,684,685],{"encoding":598},"r = 0",[573,687,689,710],{"className":688,"ariaHidden":603},[602],[573,690,692,695,698,703,707],{"className":691},[607],[573,693],{"className":694,"style":646},[611],[573,696,634],{"className":697,"style":650},[616,617],[573,699],{"className":700,"style":702},[701],"mspace","margin-right:0.2778em;",[573,704,678],{"className":705},[706],"mrel",[573,708],{"className":709,"style":702},[701],[573,711,713,717],{"className":712},[607],[573,714],{"className":715,"style":716},[611],"height:0.6444em;",[573,718,682],{"className":719},[616],": Der Kegelstumpf ist ein Kegel, ",[573,722,724,764],{"className":723},[576],[573,725,727],{"className":726},[580],[582,728,729],{"xmlns":584},[586,730,731,761],{},[589,732,733,736,738,747,750,758],{},[592,734,735],{},"V",[676,737,678],{},[739,740,741,744],"mfrac",{},[680,742,743],{},"1",[680,745,746],{},"3",[592,748,749],{},"π",[751,752,753,755],"msup",{},[592,754,594],{},[680,756,757],{},"2",[592,759,760],{},"h",[596,762,763],{"encoding":598},"V = \\frac{1}{3}\\pi R^2 h",[573,765,767,786],{"className":766,"ariaHidden":603},[602],[573,768,770,773,777,780,783],{"className":769},[607],[573,771],{"className":772,"style":612},[611],[573,774,735],{"className":775,"style":776},[616,617],"margin-right:0.2222em;",[573,778],{"className":779,"style":702},[701],[573,781,678],{"className":782},[706],[573,784],{"className":785,"style":702},[701],[573,787,789,793,883,887,920],{"className":788},[607],[573,790],{"className":791,"style":792},[611],"height:1.1901em;vertical-align:-0.345em;",[573,794,796,801,879],{"className":795},[616],[573,797],{"className":798},[799,800],"mopen","nulldelimiter",[573,802,804],{"className":803},[739],[573,805,809,870],{"className":806},[807,808],"vlist-t","vlist-t2",[573,810,813,865],{"className":811},[812],"vlist-r",[573,814,818,839,850],{"className":815,"style":817},[816],"vlist","height:0.8451em;",[573,819,821,826],{"style":820},"top:-2.655em;",[573,822],{"className":823,"style":825},[824],"pstrut","height:3em;",[573,827,833],{"className":828},[829,830,831,832],"sizing","reset-size6","size3","mtight",[573,834,836],{"className":835},[616,832],[573,837,746],{"className":838},[616,832],[573,840,842,845],{"style":841},"top:-3.23em;",[573,843],{"className":844,"style":825},[824],[573,846],{"className":847,"style":849},[848],"frac-line","border-bottom-width:0.04em;",[573,851,853,856],{"style":852},"top:-3.394em;",[573,854],{"className":855,"style":825},[824],[573,857,859],{"className":858},[829,830,831,832],[573,860,862],{"className":861},[616,832],[573,863,743],{"className":864},[616,832],[573,866,869],{"className":867},[868],"vlist-s","​",[573,871,873],{"className":872},[812],[573,874,877],{"className":875,"style":876},[816],"height:0.345em;",[573,878],{},[573,880],{"className":881},[882,800],"mclose",[573,884,749],{"className":885,"style":886},[616,617],"margin-right:0.0359em;",[573,888,890,893],{"className":889},[616],[573,891,594],{"className":892,"style":618},[616,617],[573,894,897],{"className":895},[896],"msupsub",[573,898,900],{"className":899},[807],[573,901,903],{"className":902},[812],[573,904,907],{"className":905,"style":906},[816],"height:0.8141em;",[573,908,910,914],{"style":909},"top:-3.063em;margin-right:0.05em;",[573,911],{"className":912,"style":913},[824],"height:2.7em;",[573,915,917],{"className":916},[829,830,831,832],[573,918,757],{"className":919},[616,832],[573,921,760],{"className":922},[616,617],".",[659,925,926,977,978,923],{},[573,927,929,947],{"className":928},[576],[573,930,932],{"className":931},[580],[582,933,934],{"xmlns":584},[586,935,936,944],{},[589,937,938,940,942],{},[592,939,634],{},[676,941,678],{},[592,943,594],{},[596,945,946],{"encoding":598},"r = R",[573,948,950,968],{"className":949,"ariaHidden":603},[602],[573,951,953,956,959,962,965],{"className":952},[607],[573,954],{"className":955,"style":646},[611],[573,957,634],{"className":958,"style":650},[616,617],[573,960],{"className":961,"style":702},[701],[573,963,678],{"className":964},[706],[573,966],{"className":967,"style":702},[701],[573,969,971,974],{"className":970},[607],[573,972],{"className":973,"style":612},[611],[573,975,594],{"className":976,"style":618},[616,617],": Der Körper ist ein Zylinder, ",[573,979,981,1030],{"className":980},[576],[573,982,984],{"className":983},[580],[582,985,986],{"xmlns":584},[586,987,988,1027],{},[589,989,990,992,994,1004,1007,1009,1015,1017,1019,1025],{},[592,991,735],{},[676,993,678],{},[739,995,996,1002],{},[589,997,998,1000],{},[592,999,749],{},[592,1001,760],{},[680,1003,746],{},[676,1005,1006],{},"⋅",[680,1008,746],{},[751,1010,1011,1013],{},[592,1012,594],{},[680,1014,757],{},[676,1016,678],{},[592,1018,749],{},[751,1020,1021,1023],{},[592,1022,594],{},[680,1024,757],{},[592,1026,760],{},[596,1028,1029],{"encoding":598},"V = \\frac{\\pi h}{3} \\cdot 3R^2 = \\pi R^2 h",[573,1031,1033,1051,1140,1187],{"className":1032,"ariaHidden":603},[602],[573,1034,1036,1039,1042,1045,1048],{"className":1035},[607],[573,1037],{"className":1038,"style":612},[611],[573,1040,735],{"className":1041,"style":776},[616,617],[573,1043],{"className":1044,"style":702},[701],[573,1046,678],{"className":1047},[706],[573,1049],{"className":1050,"style":702},[701],[573,1052,1054,1058,1130,1133,1137],{"className":1053},[607],[573,1055],{"className":1056,"style":1057},[611],"height:1.2251em;vertical-align:-0.345em;",[573,1059,1061,1064,1127],{"className":1060},[616],[573,1062],{"className":1063},[799,800],[573,1065,1067],{"className":1066},[739],[573,1068,1070,1119],{"className":1069},[807,808],[573,1071,1073,1116],{"className":1072},[812],[573,1074,1077,1091,1099],{"className":1075,"style":1076},[816],"height:0.8801em;",[573,1078,1079,1082],{"style":820},[573,1080],{"className":1081,"style":825},[824],[573,1083,1085],{"className":1084},[829,830,831,832],[573,1086,1088],{"className":1087},[616,832],[573,1089,746],{"className":1090},[616,832],[573,1092,1093,1096],{"style":841},[573,1094],{"className":1095,"style":825},[824],[573,1097],{"className":1098,"style":849},[848],[573,1100,1101,1104],{"style":852},[573,1102],{"className":1103,"style":825},[824],[573,1105,1107],{"className":1106},[829,830,831,832],[573,1108,1110,1113],{"className":1109},[616,832],[573,1111,749],{"className":1112,"style":886},[616,617,832],[573,1114,760],{"className":1115},[616,617,832],[573,1117,869],{"className":1118},[868],[573,1120,1122],{"className":1121},[812],[573,1123,1125],{"className":1124,"style":876},[816],[573,1126],{},[573,1128],{"className":1129},[882,800],[573,1131],{"className":1132,"style":776},[701],[573,1134,1006],{"className":1135},[1136],"mbin",[573,1138],{"className":1139,"style":776},[701],[573,1141,1143,1146,1149,1178,1181,1184],{"className":1142},[607],[573,1144],{"className":1145,"style":906},[611],[573,1147,746],{"className":1148},[616],[573,1150,1152,1155],{"className":1151},[616],[573,1153,594],{"className":1154,"style":618},[616,617],[573,1156,1158],{"className":1157},[896],[573,1159,1161],{"className":1160},[807],[573,1162,1164],{"className":1163},[812],[573,1165,1167],{"className":1166,"style":906},[816],[573,1168,1169,1172],{"style":909},[573,1170],{"className":1171,"style":913},[824],[573,1173,1175],{"className":1174},[829,830,831,832],[573,1176,757],{"className":1177},[616,832],[573,1179],{"className":1180,"style":702},[701],[573,1182,678],{"className":1183},[706],[573,1185],{"className":1186,"style":702},[701],[573,1188,1190,1193,1196,1225],{"className":1189},[607],[573,1191],{"className":1192,"style":906},[611],[573,1194,749],{"className":1195,"style":886},[616,617],[573,1197,1199,1202],{"className":1198},[616],[573,1200,594],{"className":1201,"style":618},[616,617],[573,1203,1205],{"className":1204},[896],[573,1206,1208],{"className":1207},[807],[573,1209,1211],{"className":1210},[812],[573,1212,1214],{"className":1213,"style":906},[816],[573,1215,1216,1219],{"style":909},[573,1217],{"className":1218,"style":913},[824],[573,1220,1222],{"className":1221},[829,830,831,832],[573,1223,757],{"className":1224},[616,832],[573,1226,760],{"className":1227},[616,617],[559,1229,1231],{"id":1230},"herleitung","Herleitung",[564,1233,1234,1235,1288,1289,1319,1320,1374,1375,1578],{},"Für ",[573,1236,1238,1257],{"className":1237},[576],[573,1239,1241],{"className":1240},[580],[582,1242,1243],{"xmlns":584},[586,1244,1245,1254],{},[589,1246,1247,1249,1252],{},[592,1248,594],{},[676,1250,1251],{},">",[592,1253,634],{},[596,1255,1256],{"encoding":598},"R > r",[573,1258,1260,1279],{"className":1259,"ariaHidden":603},[602],[573,1261,1263,1267,1270,1273,1276],{"className":1262},[607],[573,1264],{"className":1265,"style":1266},[611],"height:0.7224em;vertical-align:-0.0391em;",[573,1268,594],{"className":1269,"style":618},[616,617],[573,1271],{"className":1272,"style":702},[701],[573,1274,1251],{"className":1275},[706],[573,1277],{"className":1278,"style":702},[701],[573,1280,1282,1285],{"className":1281},[607],[573,1283],{"className":1284,"style":646},[611],[573,1286,634],{"className":1287,"style":650},[616,617]," ergänzt man den Kegelstumpf zum ganzen Kegel mit Höhe ",[573,1290,1292,1306],{"className":1291},[576],[573,1293,1295],{"className":1294},[580],[582,1296,1297],{"xmlns":584},[586,1298,1299,1304],{},[589,1300,1301],{},[592,1302,1303],{},"H",[596,1305,1303],{"encoding":598},[573,1307,1309],{"className":1308,"ariaHidden":603},[602],[573,1310,1312,1315],{"className":1311},[607],[573,1313],{"className":1314,"style":612},[611],[573,1316,1303],{"className":1317,"style":1318},[616,617],"margin-right:0.0813em;"," und zieht den abgeschnittenen kleinen Kegel mit Höhe ",[573,1321,1323,1342],{"className":1322},[576],[573,1324,1326],{"className":1325},[580],[582,1327,1328],{"xmlns":584},[586,1329,1330,1339],{},[589,1331,1332,1334,1337],{},[592,1333,1303],{},[676,1335,1336],{},"−",[592,1338,760],{},[596,1340,1341],{"encoding":598},"H - h",[573,1343,1345,1364],{"className":1344,"ariaHidden":603},[602],[573,1346,1348,1352,1355,1358,1361],{"className":1347},[607],[573,1349],{"className":1350,"style":1351},[611],"height:0.7667em;vertical-align:-0.0833em;",[573,1353,1303],{"className":1354,"style":1318},[616,617],[573,1356],{"className":1357,"style":776},[701],[573,1359,1336],{"className":1360},[1136],[573,1362],{"className":1363,"style":776},[701],[573,1365,1367,1371],{"className":1366},[607],[573,1368],{"className":1369,"style":1370},[611],"height:0.6944em;",[573,1372,760],{"className":1373},[616,617]," ab. Nach dem Strahlensatz gilt ",[573,1376,1378,1410],{"className":1377},[576],[573,1379,1381],{"className":1380},[580],[582,1382,1383],{"xmlns":584},[586,1384,1385,1407],{},[589,1386,1387,1399,1401],{},[739,1388,1389,1397],{},[589,1390,1391,1393,1395],{},[592,1392,1303],{},[676,1394,1336],{},[592,1396,760],{},[592,1398,1303],{},[676,1400,678],{},[739,1402,1403,1405],{},[592,1404,634],{},[592,1406,594],{},[596,1408,1409],{"encoding":598},"\\frac{H - h}{H} = \\frac{r}{R}",[573,1411,1413,1502],{"className":1412,"ariaHidden":603},[602],[573,1414,1416,1419,1493,1496,1499],{"className":1415},[607],[573,1417],{"className":1418,"style":1057},[611],[573,1420,1422,1425,1490],{"className":1421},[616],[573,1423],{"className":1424},[799,800],[573,1426,1428],{"className":1427},[739],[573,1429,1431,1482],{"className":1430},[807,808],[573,1432,1434,1479],{"className":1433},[812],[573,1435,1437,1451,1459],{"className":1436,"style":1076},[816],[573,1438,1439,1442],{"style":820},[573,1440],{"className":1441,"style":825},[824],[573,1443,1445],{"className":1444},[829,830,831,832],[573,1446,1448],{"className":1447},[616,832],[573,1449,1303],{"className":1450,"style":1318},[616,617,832],[573,1452,1453,1456],{"style":841},[573,1454],{"className":1455,"style":825},[824],[573,1457],{"className":1458,"style":849},[848],[573,1460,1461,1464],{"style":852},[573,1462],{"className":1463,"style":825},[824],[573,1465,1467],{"className":1466},[829,830,831,832],[573,1468,1470,1473,1476],{"className":1469},[616,832],[573,1471,1303],{"className":1472,"style":1318},[616,617,832],[573,1474,1336],{"className":1475},[1136,832],[573,1477,760],{"className":1478},[616,617,832],[573,1480,869],{"className":1481},[868],[573,1483,1485],{"className":1484},[812],[573,1486,1488],{"className":1487,"style":876},[816],[573,1489],{},[573,1491],{"className":1492},[882,800],[573,1494],{"className":1495,"style":702},[701],[573,1497,678],{"className":1498},[706],[573,1500],{"className":1501,"style":702},[701],[573,1503,1505,1509],{"className":1504},[607],[573,1506],{"className":1507,"style":1508},[611],"height:1.0404em;vertical-align:-0.345em;",[573,1510,1512,1515,1575],{"className":1511},[616],[573,1513],{"className":1514},[799,800],[573,1516,1518],{"className":1517},[739],[573,1519,1521,1567],{"className":1520},[807,808],[573,1522,1524,1564],{"className":1523},[812],[573,1525,1528,1542,1550],{"className":1526,"style":1527},[816],"height:0.6954em;",[573,1529,1530,1533],{"style":820},[573,1531],{"className":1532,"style":825},[824],[573,1534,1536],{"className":1535},[829,830,831,832],[573,1537,1539],{"className":1538},[616,832],[573,1540,594],{"className":1541,"style":618},[616,617,832],[573,1543,1544,1547],{"style":841},[573,1545],{"className":1546,"style":825},[824],[573,1548],{"className":1549,"style":849},[848],[573,1551,1552,1555],{"style":852},[573,1553],{"className":1554,"style":825},[824],[573,1556,1558],{"className":1557},[829,830,831,832],[573,1559,1561],{"className":1560},[616,832],[573,1562,634],{"className":1563,"style":650},[616,617,832],[573,1565,869],{"className":1566},[868],[573,1568,1570],{"className":1569},[812],[573,1571,1573],{"className":1572,"style":876},[816],[573,1574],{},[573,1576],{"className":1577},[882,800],", also",[573,1580,1583],{"className":1581},[1582],"katex-display",[573,1584,1586,1649],{"className":1585},[576],[573,1587,1589],{"className":1588},[580],[582,1590,1592],{"xmlns":584,"display":1591},"block",[586,1593,1594,1646],{},[589,1595,1596,1598,1600,1616,1619,1622,1624,1626,1628,1630],{},[592,1597,1303],{},[676,1599,678],{},[739,1601,1602,1608],{},[589,1603,1604,1606],{},[592,1605,760],{},[592,1607,594],{},[589,1609,1610,1612,1614],{},[592,1611,594],{},[676,1613,1336],{},[592,1615,634],{},[676,1617,1618],{"separator":603},",",[701,1620],{"width":1621},"2em",[592,1623,1303],{},[676,1625,1336],{},[592,1627,760],{},[676,1629,678],{},[739,1631,1632,1638],{},[589,1633,1634,1636],{},[592,1635,760],{},[592,1637,634],{},[589,1639,1640,1642,1644],{},[592,1641,594],{},[676,1643,1336],{},[592,1645,634],{},[596,1647,1648],{"encoding":598},"H = \\frac{hR}{R - r}, \\qquad H - h = \\frac{hr}{R - r}",[573,1650,1652,1670,1782,1800],{"className":1651,"ariaHidden":603},[602],[573,1653,1655,1658,1661,1664,1667],{"className":1654},[607],[573,1656],{"className":1657,"style":612},[611],[573,1659,1303],{"className":1660,"style":1318},[616,617],[573,1662],{"className":1663,"style":702},[701],[573,1665,678],{"className":1666},[706],[573,1668],{"className":1669,"style":702},[701],[573,1671,1673,1677,1758,1762,1766,1770,1773,1776,1779],{"className":1672},[607],[573,1674],{"className":1675,"style":1676},[611],"height:2.1408em;vertical-align:-0.7693em;",[573,1678,1680,1683,1755],{"className":1679},[616],[573,1681],{"className":1682},[799,800],[573,1684,1686],{"className":1685},[739],[573,1687,1689,1746],{"className":1688},[807,808],[573,1690,1692,1743],{"className":1691},[812],[573,1693,1696,1720,1728],{"className":1694,"style":1695},[816],"height:1.3714em;",[573,1697,1699,1702],{"style":1698},"top:-2.314em;",[573,1700],{"className":1701,"style":825},[824],[573,1703,1705,1708,1711,1714,1717],{"className":1704},[616],[573,1706,594],{"className":1707,"style":618},[616,617],[573,1709],{"className":1710,"style":776},[701],[573,1712,1336],{"className":1713},[1136],[573,1715],{"className":1716,"style":776},[701],[573,1718,634],{"className":1719,"style":650},[616,617],[573,1721,1722,1725],{"style":841},[573,1723],{"className":1724,"style":825},[824],[573,1726],{"className":1727,"style":849},[848],[573,1729,1731,1734],{"style":1730},"top:-3.677em;",[573,1732],{"className":1733,"style":825},[824],[573,1735,1737,1740],{"className":1736},[616],[573,1738,760],{"className":1739},[616,617],[573,1741,594],{"className":1742,"style":618},[616,617],[573,1744,869],{"className":1745},[868],[573,1747,1749],{"className":1748},[812],[573,1750,1753],{"className":1751,"style":1752},[816],"height:0.7693em;",[573,1754],{},[573,1756],{"className":1757},[882,800],[573,1759,1618],{"className":1760},[1761],"mpunct",[573,1763],{"className":1764,"style":1765},[701],"margin-right:2em;",[573,1767],{"className":1768,"style":1769},[701],"margin-right:0.1667em;",[573,1771,1303],{"className":1772,"style":1318},[616,617],[573,1774],{"className":1775,"style":776},[701],[573,1777,1336],{"className":1778},[1136],[573,1780],{"className":1781,"style":776},[701],[573,1783,1785,1788,1791,1794,1797],{"className":1784},[607],[573,1786],{"className":1787,"style":1370},[611],[573,1789,760],{"className":1790},[616,617],[573,1792],{"className":1793,"style":702},[701],[573,1795,678],{"className":1796},[706],[573,1798],{"className":1799,"style":702},[701],[573,1801,1803,1806],{"className":1802},[607],[573,1804],{"className":1805,"style":1676},[611],[573,1807,1809,1812,1880],{"className":1808},[616],[573,1810],{"className":1811},[799,800],[573,1813,1815],{"className":1814},[739],[573,1816,1818,1872],{"className":1817},[807,808],[573,1819,1821,1869],{"className":1820},[812],[573,1822,1824,1847,1855],{"className":1823,"style":1695},[816],[573,1825,1826,1829],{"style":1698},[573,1827],{"className":1828,"style":825},[824],[573,1830,1832,1835,1838,1841,1844],{"className":1831},[616],[573,1833,594],{"className":1834,"style":618},[616,617],[573,1836],{"className":1837,"style":776},[701],[573,1839,1336],{"className":1840},[1136],[573,1842],{"className":1843,"style":776},[701],[573,1845,634],{"className":1846,"style":650},[616,617],[573,1848,1849,1852],{"style":841},[573,1850],{"className":1851,"style":825},[824],[573,1853],{"className":1854,"style":849},[848],[573,1856,1857,1860],{"style":1730},[573,1858],{"className":1859,"style":825},[824],[573,1861,1863,1866],{"className":1862},[616],[573,1864,760],{"className":1865},[616,617],[573,1867,634],{"className":1868,"style":650},[616,617],[573,1870,869],{"className":1871},[868],[573,1873,1875],{"className":1874},[812],[573,1876,1878],{"className":1877,"style":1752},[816],[573,1879],{},[573,1881],{"className":1882},[882,800],[564,1884,1885],{},"Damit:",[573,1887,1889],{"className":1888},[1582],[573,1890,1892,2032],{"className":1891},[576],[573,1893,1895],{"className":1894},[580],[582,1896,1897],{"xmlns":584,"display":1591},[586,1898,1899,2029],{},[589,1900,1901,1903,1905,1911,1946,1948,1954,1956,1990,1992,2002],{},[592,1902,735],{},[676,1904,678],{},[739,1906,1907,1909],{},[592,1908,749],{},[680,1910,746],{},[589,1912,1913,1916,1922,1924,1926,1932,1935,1937,1939,1941,1944],{},[676,1914,1915],{"fence":603},"(",[751,1917,1918,1920],{},[592,1919,594],{},[680,1921,757],{},[592,1923,1303],{},[676,1925,1336],{},[751,1927,1928,1930],{},[592,1929,634],{},[680,1931,757],{},[676,1933,1915],{"stretchy":1934},"false",[592,1936,1303],{},[676,1938,1336],{},[592,1940,760],{},[676,1942,1943],{"stretchy":1934},")",[676,1945,1943],{"fence":603},[676,1947,678],{},[739,1949,1950,1952],{},[592,1951,749],{},[680,1953,746],{},[676,1955,1006],{},[739,1957,1958,1982],{},[589,1959,1960,1962],{},[592,1961,760],{},[589,1963,1964,1966,1972,1974,1980],{},[676,1965,1915],{"fence":603},[751,1967,1968,1970],{},[592,1969,594],{},[680,1971,746],{},[676,1973,1336],{},[751,1975,1976,1978],{},[592,1977,634],{},[680,1979,746],{},[676,1981,1943],{"fence":603},[589,1983,1984,1986,1988],{},[592,1985,594],{},[676,1987,1336],{},[592,1989,634],{},[676,1991,678],{},[739,1993,1994,2000],{},[589,1995,1996,1998],{},[592,1997,749],{},[592,1999,760],{},[680,2001,746],{},[589,2003,2004,2006,2012,2015,2017,2019,2021,2027],{},[676,2005,1915],{"fence":603},[751,2007,2008,2010],{},[592,2009,594],{},[680,2011,757],{},[676,2013,2014],{},"+",[592,2016,594],{},[592,2018,634],{},[676,2020,2014],{},[751,2022,2023,2025],{},[592,2024,634],{},[680,2026,757],{},[676,2028,1943],{"fence":603},[596,2030,2031],{"encoding":598},"V = \\frac{\\pi}{3}\\left(R^2 H - r^2 (H - h)\\right) = \\frac{\\pi}{3} \\cdot \\frac{h\\left(R^3 - r^3\\right)}{R - r} = \\frac{\\pi h}{3}\\left(R^2 + Rr + r^2\\right)",[573,2033,2035,2053,2249,2326,2503],{"className":2034,"ariaHidden":603},[602],[573,2036,2038,2041,2044,2047,2050],{"className":2037},[607],[573,2039],{"className":2040,"style":612},[611],[573,2042,735],{"className":2043,"style":776},[616,617],[573,2045],{"className":2046,"style":702},[701],[573,2048,678],{"className":2049},[706],[573,2051],{"className":2052,"style":702},[701],[573,2054,2056,2060,2124,2127,2240,2243,2246],{"className":2055},[607],[573,2057],{"className":2058,"style":2059},[611],"height:1.7936em;vertical-align:-0.686em;",[573,2061,2063,2066,2121],{"className":2062},[616],[573,2064],{"className":2065},[799,800],[573,2067,2069],{"className":2068},[739],[573,2070,2072,2112],{"className":2071},[807,808],[573,2073,2075,2109],{"className":2074},[812],[573,2076,2079,2090,2098],{"className":2077,"style":2078},[816],"height:1.1076em;",[573,2080,2081,2084],{"style":1698},[573,2082],{"className":2083,"style":825},[824],[573,2085,2087],{"className":2086},[616],[573,2088,746],{"className":2089},[616],[573,2091,2092,2095],{"style":841},[573,2093],{"className":2094,"style":825},[824],[573,2096],{"className":2097,"style":849},[848],[573,2099,2100,2103],{"style":1730},[573,2101],{"className":2102,"style":825},[824],[573,2104,2106],{"className":2105},[616],[573,2107,749],{"className":2108,"style":886},[616,617],[573,2110,869],{"className":2111},[868],[573,2113,2115],{"className":2114},[812],[573,2116,2119],{"className":2117,"style":2118},[816],"height:0.686em;",[573,2120],{},[573,2122],{"className":2123},[882,800],[573,2125],{"className":2126,"style":1769},[701],[573,2128,2131,2141,2172,2175,2178,2181,2184,2213,2216,2219,2222,2225,2228,2231,2234],{"className":2129},[2130],"minner",[573,2132,2136],{"className":2133,"style":2135},[799,2134],"delimcenter","top:0em;",[573,2137,1915],{"className":2138},[2139,2140],"delimsizing","size1",[573,2142,2144,2147],{"className":2143},[616],[573,2145,594],{"className":2146,"style":618},[616,617],[573,2148,2150],{"className":2149},[896],[573,2151,2153],{"className":2152},[807],[573,2154,2156],{"className":2155},[812],[573,2157,2160],{"className":2158,"style":2159},[816],"height:0.8641em;",[573,2161,2163,2166],{"style":2162},"top:-3.113em;margin-right:0.05em;",[573,2164],{"className":2165,"style":913},[824],[573,2167,2169],{"className":2168},[829,830,831,832],[573,2170,757],{"className":2171},[616,832],[573,2173,1303],{"className":2174,"style":1318},[616,617],[573,2176],{"className":2177,"style":776},[701],[573,2179,1336],{"className":2180},[1136],[573,2182],{"className":2183,"style":776},[701],[573,2185,2187,2190],{"className":2186},[616],[573,2188,634],{"className":2189,"style":650},[616,617],[573,2191,2193],{"className":2192},[896],[573,2194,2196],{"className":2195},[807],[573,2197,2199],{"className":2198},[812],[573,2200,2202],{"className":2201,"style":2159},[816],[573,2203,2204,2207],{"style":2162},[573,2205],{"className":2206,"style":913},[824],[573,2208,2210],{"className":2209},[829,830,831,832],[573,2211,757],{"className":2212},[616,832],[573,2214,1915],{"className":2215},[799],[573,2217,1303],{"className":2218,"style":1318},[616,617],[573,2220],{"className":2221,"style":776},[701],[573,2223,1336],{"className":2224},[1136],[573,2226],{"className":2227,"style":776},[701],[573,2229,760],{"className":2230},[616,617],[573,2232,1943],{"className":2233},[882],[573,2235,2237],{"className":2236,"style":2135},[882,2134],[573,2238,1943],{"className":2239},[2139,2140],[573,2241],{"className":2242,"style":702},[701],[573,2244,678],{"className":2245},[706],[573,2247],{"className":2248,"style":702},[701],[573,2250,2252,2255,2317,2320,2323],{"className":2251},[607],[573,2253],{"className":2254,"style":2059},[611],[573,2256,2258,2261,2314],{"className":2257},[616],[573,2259],{"className":2260},[799,800],[573,2262,2264],{"className":2263},[739],[573,2265,2267,2306],{"className":2266},[807,808],[573,2268,2270,2303],{"className":2269},[812],[573,2271,2273,2284,2292],{"className":2272,"style":2078},[816],[573,2274,2275,2278],{"style":1698},[573,2276],{"className":2277,"style":825},[824],[573,2279,2281],{"className":2280},[616],[573,2282,746],{"className":2283},[616],[573,2285,2286,2289],{"style":841},[573,2287],{"className":2288,"style":825},[824],[573,2290],{"className":2291,"style":849},[848],[573,2293,2294,2297],{"style":1730},[573,2295],{"className":2296,"style":825},[824],[573,2298,2300],{"className":2299},[616],[573,2301,749],{"className":2302,"style":886},[616,617],[573,2304,869],{"className":2305},[868],[573,2307,2309],{"className":2308},[812],[573,2310,2312],{"className":2311,"style":2118},[816],[573,2313],{},[573,2315],{"className":2316},[882,800],[573,2318],{"className":2319,"style":776},[701],[573,2321,1006],{"className":2322},[1136],[573,2324],{"className":2325,"style":776},[701],[573,2327,2329,2333,2494,2497,2500],{"className":2328},[607],[573,2330],{"className":2331,"style":2332},[611],"height:2.3593em;vertical-align:-0.7693em;",[573,2334,2336,2339,2491],{"className":2335},[616],[573,2337],{"className":2338},[799,800],[573,2340,2342],{"className":2341},[739],[573,2343,2345,2483],{"className":2344},[807,808],[573,2346,2348,2480],{"className":2347},[812],[573,2349,2352,2375,2383],{"className":2350,"style":2351},[816],"height:1.59em;",[573,2353,2354,2357],{"style":1698},[573,2355],{"className":2356,"style":825},[824],[573,2358,2360,2363,2366,2369,2372],{"className":2359},[616],[573,2361,594],{"className":2362,"style":618},[616,617],[573,2364],{"className":2365,"style":776},[701],[573,2367,1336],{"className":2368},[1136],[573,2370],{"className":2371,"style":776},[701],[573,2373,634],{"className":2374,"style":650},[616,617],[573,2376,2377,2380],{"style":841},[573,2378],{"className":2379,"style":825},[824],[573,2381],{"className":2382,"style":849},[848],[573,2384,2386,2389],{"style":2385},"top:-3.74em;",[573,2387],{"className":2388,"style":825},[824],[573,2390,2392,2395,2398],{"className":2391},[616],[573,2393,760],{"className":2394},[616,617],[573,2396],{"className":2397,"style":1769},[701],[573,2399,2401,2407,2436,2439,2442,2445,2474],{"className":2400},[2130],[573,2402,2404],{"className":2403,"style":2135},[799,2134],[573,2405,1915],{"className":2406},[2139,2140],[573,2408,2410,2413],{"className":2409},[616],[573,2411,594],{"className":2412,"style":618},[616,617],[573,2414,2416],{"className":2415},[896],[573,2417,2419],{"className":2418},[807],[573,2420,2422],{"className":2421},[812],[573,2423,2425],{"className":2424,"style":906},[816],[573,2426,2427,2430],{"style":909},[573,2428],{"className":2429,"style":913},[824],[573,2431,2433],{"className":2432},[829,830,831,832],[573,2434,746],{"className":2435},[616,832],[573,2437],{"className":2438,"style":776},[701],[573,2440,1336],{"className":2441},[1136],[573,2443],{"className":2444,"style":776},[701],[573,2446,2448,2451],{"className":2447},[616],[573,2449,634],{"className":2450,"style":650},[616,617],[573,2452,2454],{"className":2453},[896],[573,2455,2457],{"className":2456},[807],[573,2458,2460],{"className":2459},[812],[573,2461,2463],{"className":2462,"style":906},[816],[573,2464,2465,2468],{"style":909},[573,2466],{"className":2467,"style":913},[824],[573,2469,2471],{"className":2470},[829,830,831,832],[573,2472,746],{"className":2473},[616,832],[573,2475,2477],{"className":2476,"style":2135},[882,2134],[573,2478,1943],{"className":2479},[2139,2140],[573,2481,869],{"className":2482},[868],[573,2484,2486],{"className":2485},[812],[573,2487,2489],{"className":2488,"style":1752},[816],[573,2490],{},[573,2492],{"className":2493},[882,800],[573,2495],{"className":2496,"style":702},[701],[573,2498,678],{"className":2499},[706],[573,2501],{"className":2502,"style":702},[701],[573,2504,2506,2510,2575,2578],{"className":2505},[607],[573,2507],{"className":2508,"style":2509},[611],"height:2.0574em;vertical-align:-0.686em;",[573,2511,2513,2516,2572],{"className":2512},[616],[573,2514],{"className":2515},[799,800],[573,2517,2519],{"className":2518},[739],[573,2520,2522,2564],{"className":2521},[807,808],[573,2523,2525,2561],{"className":2524},[812],[573,2526,2528,2539,2547],{"className":2527,"style":1695},[816],[573,2529,2530,2533],{"style":1698},[573,2531],{"className":2532,"style":825},[824],[573,2534,2536],{"className":2535},[616],[573,2537,746],{"className":2538},[616],[573,2540,2541,2544],{"style":841},[573,2542],{"className":2543,"style":825},[824],[573,2545],{"className":2546,"style":849},[848],[573,2548,2549,2552],{"style":1730},[573,2550],{"className":2551,"style":825},[824],[573,2553,2555,2558],{"className":2554},[616],[573,2556,749],{"className":2557,"style":886},[616,617],[573,2559,760],{"className":2560},[616,617],[573,2562,869],{"className":2563},[868],[573,2565,2567],{"className":2566},[812],[573,2568,2570],{"className":2569,"style":2118},[816],[573,2571],{},[573,2573],{"className":2574},[882,800],[573,2576],{"className":2577,"style":1769},[701],[573,2579,2581,2587,2616,2619,2622,2625,2628,2631,2634,2637,2640,2669],{"className":2580},[2130],[573,2582,2584],{"className":2583,"style":2135},[799,2134],[573,2585,1915],{"className":2586},[2139,2140],[573,2588,2590,2593],{"className":2589},[616],[573,2591,594],{"className":2592,"style":618},[616,617],[573,2594,2596],{"className":2595},[896],[573,2597,2599],{"className":2598},[807],[573,2600,2602],{"className":2601},[812],[573,2603,2605],{"className":2604,"style":2159},[816],[573,2606,2607,2610],{"style":2162},[573,2608],{"className":2609,"style":913},[824],[573,2611,2613],{"className":2612},[829,830,831,832],[573,2614,757],{"className":2615},[616,832],[573,2617],{"className":2618,"style":776},[701],[573,2620,2014],{"className":2621},[1136],[573,2623],{"className":2624,"style":776},[701],[573,2626,594],{"className":2627,"style":618},[616,617],[573,2629,634],{"className":2630,"style":650},[616,617],[573,2632],{"className":2633,"style":776},[701],[573,2635,2014],{"className":2636},[1136],[573,2638],{"className":2639,"style":776},[701],[573,2641,2643,2646],{"className":2642},[616],[573,2644,634],{"className":2645,"style":650},[616,617],[573,2647,2649],{"className":2648},[896],[573,2650,2652],{"className":2651},[807],[573,2653,2655],{"className":2654},[812],[573,2656,2658],{"className":2657,"style":2159},[816],[573,2659,2660,2663],{"style":2162},[573,2661],{"className":2662,"style":913},[824],[573,2664,2666],{"className":2665},[829,830,831,832],[573,2667,757],{"className":2668},[616,832],[573,2670,2672],{"className":2671,"style":2135},[882,2134],[573,2673,1943],{"className":2674},[2139,2140],[564,2676,2677,2678,2970],{},"Im letzten Schritt wurde ",[573,2679,2681,2743],{"className":2680},[576],[573,2682,2684],{"className":2683},[580],[582,2685,2686],{"xmlns":584},[586,2687,2688,2740],{},[589,2689,2690,2696,2698,2704,2706,2708,2710,2712,2714,2716,2718,2724,2726,2728,2730,2732,2738],{},[751,2691,2692,2694],{},[592,2693,594],{},[680,2695,746],{},[676,2697,1336],{},[751,2699,2700,2702],{},[592,2701,634],{},[680,2703,746],{},[676,2705,678],{},[676,2707,1915],{"stretchy":1934},[592,2709,594],{},[676,2711,1336],{},[592,2713,634],{},[676,2715,1943],{"stretchy":1934},[676,2717,1915],{"stretchy":1934},[751,2719,2720,2722],{},[592,2721,594],{},[680,2723,757],{},[676,2725,2014],{},[592,2727,594],{},[592,2729,634],{},[676,2731,2014],{},[751,2733,2734,2736],{},[592,2735,634],{},[680,2737,757],{},[676,2739,1943],{"stretchy":1934},[596,2741,2742],{"encoding":598},"R^3 - r^3 = (R - r)(R^2 + Rr + r^2)",[573,2744,2746,2791,2835,2857,2911,2932],{"className":2745,"ariaHidden":603},[602],[573,2747,2749,2753,2782,2785,2788],{"className":2748},[607],[573,2750],{"className":2751,"style":2752},[611],"height:0.8974em;vertical-align:-0.0833em;",[573,2754,2756,2759],{"className":2755},[616],[573,2757,594],{"className":2758,"style":618},[616,617],[573,2760,2762],{"className":2761},[896],[573,2763,2765],{"className":2764},[807],[573,2766,2768],{"className":2767},[812],[573,2769,2771],{"className":2770,"style":906},[816],[573,2772,2773,2776],{"style":909},[573,2774],{"className":2775,"style":913},[824],[573,2777,2779],{"className":2778},[829,830,831,832],[573,2780,746],{"className":2781},[616,832],[573,2783],{"className":2784,"style":776},[701],[573,2786,1336],{"className":2787},[1136],[573,2789],{"className":2790,"style":776},[701],[573,2792,2794,2797,2826,2829,2832],{"className":2793},[607],[573,2795],{"className":2796,"style":906},[611],[573,2798,2800,2803],{"className":2799},[616],[573,2801,634],{"className":2802,"style":650},[616,617],[573,2804,2806],{"className":2805},[896],[573,2807,2809],{"className":2808},[807],[573,2810,2812],{"className":2811},[812],[573,2813,2815],{"className":2814,"style":906},[816],[573,2816,2817,2820],{"style":909},[573,2818],{"className":2819,"style":913},[824],[573,2821,2823],{"className":2822},[829,830,831,832],[573,2824,746],{"className":2825},[616,832],[573,2827],{"className":2828,"style":702},[701],[573,2830,678],{"className":2831},[706],[573,2833],{"className":2834,"style":702},[701],[573,2836,2838,2842,2845,2848,2851,2854],{"className":2837},[607],[573,2839],{"className":2840,"style":2841},[611],"height:1em;vertical-align:-0.25em;",[573,2843,1915],{"className":2844},[799],[573,2846,594],{"className":2847,"style":618},[616,617],[573,2849],{"className":2850,"style":776},[701],[573,2852,1336],{"className":2853},[1136],[573,2855],{"className":2856,"style":776},[701],[573,2858,2860,2864,2867,2870,2873,2902,2905,2908],{"className":2859},[607],[573,2861],{"className":2862,"style":2863},[611],"height:1.0641em;vertical-align:-0.25em;",[573,2865,634],{"className":2866,"style":650},[616,617],[573,2868,1943],{"className":2869},[882],[573,2871,1915],{"className":2872},[799],[573,2874,2876,2879],{"className":2875},[616],[573,2877,594],{"className":2878,"style":618},[616,617],[573,2880,2882],{"className":2881},[896],[573,2883,2885],{"className":2884},[807],[573,2886,2888],{"className":2887},[812],[573,2889,2891],{"className":2890,"style":906},[816],[573,2892,2893,2896],{"style":909},[573,2894],{"className":2895,"style":913},[824],[573,2897,2899],{"className":2898},[829,830,831,832],[573,2900,757],{"className":2901},[616,832],[573,2903],{"className":2904,"style":776},[701],[573,2906,2014],{"className":2907},[1136],[573,2909],{"className":2910,"style":776},[701],[573,2912,2914,2917,2920,2923,2926,2929],{"className":2913},[607],[573,2915],{"className":2916,"style":1351},[611],[573,2918,594],{"className":2919,"style":618},[616,617],[573,2921,634],{"className":2922,"style":650},[616,617],[573,2924],{"className":2925,"style":776},[701],[573,2927,2014],{"className":2928},[1136],[573,2930],{"className":2931,"style":776},[701],[573,2933,2935,2938,2967],{"className":2934},[607],[573,2936],{"className":2937,"style":2863},[611],[573,2939,2941,2944],{"className":2940},[616],[573,2942,634],{"className":2943,"style":650},[616,617],[573,2945,2947],{"className":2946},[896],[573,2948,2950],{"className":2949},[807],[573,2951,2953],{"className":2952},[812],[573,2954,2956],{"className":2955,"style":906},[816],[573,2957,2958,2961],{"style":909},[573,2959],{"className":2960,"style":913},[824],[573,2962,2964],{"className":2963},[829,830,831,832],[573,2965,757],{"className":2966},[616,832],[573,2968,1943],{"className":2969},[882]," verwendet.",[559,2972,2974],{"id":2973},"beispiele","Beispiele",[564,2976,2977,2978,3047,3048,3112,3113,3178],{},"Ein Kegelstumpf hat ",[573,2979,2981,3007],{"className":2980},[576],[573,2982,2984],{"className":2983},[580],[582,2985,2986],{"xmlns":584},[586,2987,2988,3004],{},[589,2989,2990,2992,2994,2997,3001],{},[592,2991,594],{},[676,2993,678],{},[680,2995,2996],{},"4",[2998,2999,3000],"mtext",{}," ",[2998,3002,3003],{},"cm",[596,3005,3006],{"encoding":598},"R = 4\\,\\text{cm}",[573,3008,3010,3028],{"className":3009,"ariaHidden":603},[602],[573,3011,3013,3016,3019,3022,3025],{"className":3012},[607],[573,3014],{"className":3015,"style":612},[611],[573,3017,594],{"className":3018,"style":618},[616,617],[573,3020],{"className":3021,"style":702},[701],[573,3023,678],{"className":3024},[706],[573,3026],{"className":3027,"style":702},[701],[573,3029,3031,3034,3037,3040],{"className":3030},[607],[573,3032],{"className":3033,"style":716},[611],[573,3035,2996],{"className":3036},[616],[573,3038],{"className":3039,"style":1769},[701],[573,3041,3044],{"className":3042},[616,3043],"text",[573,3045,3003],{"className":3046},[616],", ",[573,3049,3051,3073],{"className":3050},[576],[573,3052,3054],{"className":3053},[580],[582,3055,3056],{"xmlns":584},[586,3057,3058,3070],{},[589,3059,3060,3062,3064,3066,3068],{},[592,3061,634],{},[676,3063,678],{},[680,3065,757],{},[2998,3067,3000],{},[2998,3069,3003],{},[596,3071,3072],{"encoding":598},"r = 2\\,\\text{cm}",[573,3074,3076,3094],{"className":3075,"ariaHidden":603},[602],[573,3077,3079,3082,3085,3088,3091],{"className":3078},[607],[573,3080],{"className":3081,"style":646},[611],[573,3083,634],{"className":3084,"style":650},[616,617],[573,3086],{"className":3087,"style":702},[701],[573,3089,678],{"className":3090},[706],[573,3092],{"className":3093,"style":702},[701],[573,3095,3097,3100,3103,3106],{"className":3096},[607],[573,3098],{"className":3099,"style":716},[611],[573,3101,757],{"className":3102},[616],[573,3104],{"className":3105,"style":1769},[701],[573,3107,3109],{"className":3108},[616,3043],[573,3110,3003],{"className":3111},[616]," und ",[573,3114,3116,3139],{"className":3115},[576],[573,3117,3119],{"className":3118},[580],[582,3120,3121],{"xmlns":584},[586,3122,3123,3136],{},[589,3124,3125,3127,3129,3132,3134],{},[592,3126,760],{},[676,3128,678],{},[680,3130,3131],{},"6",[2998,3133,3000],{},[2998,3135,3003],{},[596,3137,3138],{"encoding":598},"h = 6\\,\\text{cm}",[573,3140,3142,3160],{"className":3141,"ariaHidden":603},[602],[573,3143,3145,3148,3151,3154,3157],{"className":3144},[607],[573,3146],{"className":3147,"style":1370},[611],[573,3149,760],{"className":3150},[616,617],[573,3152],{"className":3153,"style":702},[701],[573,3155,678],{"className":3156},[706],[573,3158],{"className":3159,"style":702},[701],[573,3161,3163,3166,3169,3172],{"className":3162},[607],[573,3164],{"className":3165,"style":716},[611],[573,3167,3131],{"className":3168},[616],[573,3170],{"className":3171,"style":1769},[701],[573,3173,3175],{"className":3174},[616,3043],[573,3176,3003],{"className":3177},[616],":",[573,3180,3182],{"className":3181},[1582],[573,3183,3185,3297],{"className":3184},[576],[573,3186,3188],{"className":3187},[580],[582,3189,3190],{"xmlns":584,"display":1591},[586,3191,3192,3294],{},[589,3193,3194,3196,3198,3210,3238,3240,3246,3248,3250,3252,3254,3257,3259,3265,3267,3270,3272,3274,3280,3283,3286,3288],{},[592,3195,735],{},[676,3197,678],{},[739,3199,3200,3208],{},[589,3201,3202,3204,3206],{},[592,3203,749],{},[676,3205,1006],{},[680,3207,3131],{},[680,3209,746],{},[589,3211,3212,3214,3220,3222,3224,3226,3228,3230,3236],{},[676,3213,1915],{"fence":603},[751,3215,3216,3218],{},[680,3217,2996],{},[680,3219,757],{},[676,3221,2014],{},[680,3223,2996],{},[676,3225,1006],{},[680,3227,757],{},[676,3229,2014],{},[751,3231,3232,3234],{},[680,3233,757],{},[680,3235,757],{},[676,3237,1943],{"fence":603},[2998,3239,3000],{},[751,3241,3242,3244],{},[2998,3243,3003],{},[680,3245,746],{},[676,3247,678],{},[680,3249,757],{},[592,3251,749],{},[676,3253,1006],{},[680,3255,3256],{},"28",[2998,3258,3000],{},[751,3260,3261,3263],{},[2998,3262,3003],{},[680,3264,746],{},[676,3266,678],{},[680,3268,3269],{},"56",[592,3271,749],{},[2998,3273,3000],{},[751,3275,3276,3278],{},[2998,3277,3003],{},[680,3279,746],{},[676,3281,3282],{},"≈",[680,3284,3285],{},"175,93",[2998,3287,3000],{},[751,3289,3290,3292],{},[2998,3291,3003],{},[680,3293,746],{},[596,3295,3296],{"encoding":598},"V = \\frac{\\pi \\cdot 6}{3}\\left(4^2 + 4 \\cdot 2 + 2^2\\right)\\,\\text{cm}^3 = 2\\pi \\cdot 28\\,\\text{cm}^3 = 56\\pi\\,\\text{cm}^3 \\approx 175{,}93\\,\\text{cm}^3",[573,3298,3300,3318,3556,3577,3630,3686],{"className":3299,"ariaHidden":603},[602],[573,3301,3303,3306,3309,3312,3315],{"className":3302},[607],[573,3304],{"className":3305,"style":612},[611],[573,3307,735],{"className":3308,"style":776},[616,617],[573,3310],{"className":3311,"style":702},[701],[573,3313,678],{"className":3314},[706],[573,3316],{"className":3317,"style":702},[701],[573,3319,3321,3325,3400,3403,3509,3512,3515,3547,3550,3553],{"className":3320},[607],[573,3322],{"className":3323,"style":3324},[611],"height:2.0074em;vertical-align:-0.686em;",[573,3326,3328,3331,3397],{"className":3327},[616],[573,3329],{"className":3330},[799,800],[573,3332,3334],{"className":3333},[739],[573,3335,3337,3389],{"className":3336},[807,808],[573,3338,3340,3386],{"className":3339},[812],[573,3341,3344,3355,3363],{"className":3342,"style":3343},[816],"height:1.3214em;",[573,3345,3346,3349],{"style":1698},[573,3347],{"className":3348,"style":825},[824],[573,3350,3352],{"className":3351},[616],[573,3353,746],{"className":3354},[616],[573,3356,3357,3360],{"style":841},[573,3358],{"className":3359,"style":825},[824],[573,3361],{"className":3362,"style":849},[848],[573,3364,3365,3368],{"style":1730},[573,3366],{"className":3367,"style":825},[824],[573,3369,3371,3374,3377,3380,3383],{"className":3370},[616],[573,3372,749],{"className":3373,"style":886},[616,617],[573,3375],{"className":3376,"style":776},[701],[573,3378,1006],{"className":3379},[1136],[573,3381],{"className":3382,"style":776},[701],[573,3384,3131],{"className":3385},[616],[573,3387,869],{"className":3388},[868],[573,3390,3392],{"className":3391},[812],[573,3393,3395],{"className":3394,"style":2118},[816],[573,3396],{},[573,3398],{"className":3399},[882,800],[573,3401],{"className":3402,"style":1769},[701],[573,3404,3406,3412,3441,3444,3447,3450,3453,3456,3459,3462,3465,3468,3471,3474,3503],{"className":3405},[2130],[573,3407,3409],{"className":3408,"style":2135},[799,2134],[573,3410,1915],{"className":3411},[2139,2140],[573,3413,3415,3418],{"className":3414},[616],[573,3416,2996],{"className":3417},[616],[573,3419,3421],{"className":3420},[896],[573,3422,3424],{"className":3423},[807],[573,3425,3427],{"className":3426},[812],[573,3428,3430],{"className":3429,"style":2159},[816],[573,3431,3432,3435],{"style":2162},[573,3433],{"className":3434,"style":913},[824],[573,3436,3438],{"className":3437},[829,830,831,832],[573,3439,757],{"className":3440},[616,832],[573,3442],{"className":3443,"style":776},[701],[573,3445,2014],{"className":3446},[1136],[573,3448],{"className":3449,"style":776},[701],[573,3451,2996],{"className":3452},[616],[573,3454],{"className":3455,"style":776},[701],[573,3457,1006],{"className":3458},[1136],[573,3460],{"className":3461,"style":776},[701],[573,3463,757],{"className":3464},[616],[573,3466],{"className":3467,"style":776},[701],[573,3469,2014],{"className":3470},[1136],[573,3472],{"className":3473,"style":776},[701],[573,3475,3477,3480],{"className":3476},[616],[573,3478,757],{"className":3479},[616],[573,3481,3483],{"className":3482},[896],[573,3484,3486],{"className":3485},[807],[573,3487,3489],{"className":3488},[812],[573,3490,3492],{"className":3491,"style":2159},[816],[573,3493,3494,3497],{"style":2162},[573,3495],{"className":3496,"style":913},[824],[573,3498,3500],{"className":3499},[829,830,831,832],[573,3501,757],{"className":3502},[616,832],[573,3504,3506],{"className":3505,"style":2135},[882,2134],[573,3507,1943],{"className":3508},[2139,2140],[573,3510],{"className":3511,"style":1769},[701],[573,3513],{"className":3514,"style":1769},[701],[573,3516,3518,3524],{"className":3517},[616],[573,3519,3521],{"className":3520},[616,3043],[573,3522,3003],{"className":3523},[616],[573,3525,3527],{"className":3526},[896],[573,3528,3530],{"className":3529},[807],[573,3531,3533],{"className":3532},[812],[573,3534,3536],{"className":3535,"style":2159},[816],[573,3537,3538,3541],{"style":2162},[573,3539],{"className":3540,"style":913},[824],[573,3542,3544],{"className":3543},[829,830,831,832],[573,3545,746],{"className":3546},[616,832],[573,3548],{"className":3549,"style":702},[701],[573,3551,678],{"className":3552},[706],[573,3554],{"className":3555,"style":702},[701],[573,3557,3559,3562,3565,3568,3571,3574],{"className":3558},[607],[573,3560],{"className":3561,"style":716},[611],[573,3563,757],{"className":3564},[616],[573,3566,749],{"className":3567,"style":886},[616,617],[573,3569],{"className":3570,"style":776},[701],[573,3572,1006],{"className":3573},[1136],[573,3575],{"className":3576,"style":776},[701],[573,3578,3580,3583,3586,3589,3621,3624,3627],{"className":3579},[607],[573,3581],{"className":3582,"style":2159},[611],[573,3584,3256],{"className":3585},[616],[573,3587],{"className":3588,"style":1769},[701],[573,3590,3592,3598],{"className":3591},[616],[573,3593,3595],{"className":3594},[616,3043],[573,3596,3003],{"className":3597},[616],[573,3599,3601],{"className":3600},[896],[573,3602,3604],{"className":3603},[807],[573,3605,3607],{"className":3606},[812],[573,3608,3610],{"className":3609,"style":2159},[816],[573,3611,3612,3615],{"style":2162},[573,3613],{"className":3614,"style":913},[824],[573,3616,3618],{"className":3617},[829,830,831,832],[573,3619,746],{"className":3620},[616,832],[573,3622],{"className":3623,"style":702},[701],[573,3625,678],{"className":3626},[706],[573,3628],{"className":3629,"style":702},[701],[573,3631,3633,3636,3639,3642,3645,3677,3680,3683],{"className":3632},[607],[573,3634],{"className":3635,"style":2159},[611],[573,3637,3269],{"className":3638},[616],[573,3640,749],{"className":3641,"style":886},[616,617],[573,3643],{"className":3644,"style":1769},[701],[573,3646,3648,3654],{"className":3647},[616],[573,3649,3651],{"className":3650},[616,3043],[573,3652,3003],{"className":3653},[616],[573,3655,3657],{"className":3656},[896],[573,3658,3660],{"className":3659},[807],[573,3661,3663],{"className":3662},[812],[573,3664,3666],{"className":3665,"style":2159},[816],[573,3667,3668,3671],{"style":2162},[573,3669],{"className":3670,"style":913},[824],[573,3672,3674],{"className":3673},[829,830,831,832],[573,3675,746],{"className":3676},[616,832],[573,3678],{"className":3679,"style":702},[701],[573,3681,3282],{"className":3682},[706],[573,3684],{"className":3685,"style":702},[701],[573,3687,3689,3693,3697,3703,3707,3710],{"className":3688},[607],[573,3690],{"className":3691,"style":3692},[611],"height:1.0585em;vertical-align:-0.1944em;",[573,3694,3696],{"className":3695},[616],"175",[573,3698,3700],{"className":3699},[616],[573,3701,1618],{"className":3702},[1761],[573,3704,3706],{"className":3705},[616],"93",[573,3708],{"className":3709,"style":1769},[701],[573,3711,3713,3719],{"className":3712},[616],[573,3714,3716],{"className":3715},[616,3043],[573,3717,3003],{"className":3718},[616],[573,3720,3722],{"className":3721},[896],[573,3723,3725],{"className":3724},[807],[573,3726,3728],{"className":3727},[812],[573,3729,3731],{"className":3730,"style":2159},[816],[573,3732,3733,3736],{"style":2162},[573,3734],{"className":3735,"style":913},[824],[573,3737,3739],{"className":3738},[829,830,831,832],[573,3740,746],{"className":3741},[616,832],[564,3743,3744,3745,3788,3789,3832,3833,3876],{},"Ein Eimer ist ",[573,3746,3748,3767],{"className":3747},[576],[573,3749,3751],{"className":3750},[580],[582,3752,3753],{"xmlns":584},[586,3754,3755,3764],{},[589,3756,3757,3760,3762],{},[680,3758,3759],{},"30",[2998,3761,3000],{},[2998,3763,3003],{},[596,3765,3766],{"encoding":598},"30\\,\\text{cm}",[573,3768,3770],{"className":3769,"ariaHidden":603},[602],[573,3771,3773,3776,3779,3782],{"className":3772},[607],[573,3774],{"className":3775,"style":716},[611],[573,3777,3759],{"className":3778},[616],[573,3780],{"className":3781,"style":1769},[701],[573,3783,3785],{"className":3784},[616,3043],[573,3786,3003],{"className":3787},[616]," hoch, hat oben einen Radius von ",[573,3790,3792,3811],{"className":3791},[576],[573,3793,3795],{"className":3794},[580],[582,3796,3797],{"xmlns":584},[586,3798,3799,3808],{},[589,3800,3801,3804,3806],{},[680,3802,3803],{},"15",[2998,3805,3000],{},[2998,3807,3003],{},[596,3809,3810],{"encoding":598},"15\\,\\text{cm}",[573,3812,3814],{"className":3813,"ariaHidden":603},[602],[573,3815,3817,3820,3823,3826],{"className":3816},[607],[573,3818],{"className":3819,"style":716},[611],[573,3821,3803],{"className":3822},[616],[573,3824],{"className":3825,"style":1769},[701],[573,3827,3829],{"className":3828},[616,3043],[573,3830,3003],{"className":3831},[616]," und unten von ",[573,3834,3836,3855],{"className":3835},[576],[573,3837,3839],{"className":3838},[580],[582,3840,3841],{"xmlns":584},[586,3842,3843,3852],{},[589,3844,3845,3848,3850],{},[680,3846,3847],{},"10",[2998,3849,3000],{},[2998,3851,3003],{},[596,3853,3854],{"encoding":598},"10\\,\\text{cm}",[573,3856,3858],{"className":3857,"ariaHidden":603},[602],[573,3859,3861,3864,3867,3870],{"className":3860},[607],[573,3862],{"className":3863,"style":716},[611],[573,3865,3847],{"className":3866},[616],[573,3868],{"className":3869,"style":1769},[701],[573,3871,3873],{"className":3872},[616,3043],[573,3874,3003],{"className":3875},[616],". Für die Formel ist egal, ob der größere Kreis oben oder unten liegt:",[573,3878,3880],{"className":3879},[1582],[573,3881,3883,3980],{"className":3882},[576],[573,3884,3886],{"className":3885},[580],[582,3887,3888],{"xmlns":584,"display":1591},[586,3889,3890,3977],{},[589,3891,3892,3894,3896,3908,3936,3938,3944,3946,3949,3951,3953,3959,3961,3964,3966,3969,3971],{},[592,3893,735],{},[676,3895,678],{},[739,3897,3898,3906],{},[589,3899,3900,3902,3904],{},[592,3901,749],{},[676,3903,1006],{},[680,3905,3759],{},[680,3907,746],{},[589,3909,3910,3912,3918,3920,3922,3924,3926,3928,3934],{},[676,3911,1915],{"fence":603},[751,3913,3914,3916],{},[680,3915,3803],{},[680,3917,757],{},[676,3919,2014],{},[680,3921,3803],{},[676,3923,1006],{},[680,3925,3847],{},[676,3927,2014],{},[751,3929,3930,3932],{},[680,3931,3847],{},[680,3933,757],{},[676,3935,1943],{"fence":603},[2998,3937,3000],{},[751,3939,3940,3942],{},[2998,3941,3003],{},[680,3943,746],{},[676,3945,678],{},[680,3947,3948],{},"4750",[592,3950,749],{},[2998,3952,3000],{},[751,3954,3955,3957],{},[2998,3956,3003],{},[680,3958,746],{},[676,3960,3282],{},[680,3962,3963],{},"14",[2998,3965,3000],{},[680,3967,3968],{},"923",[2998,3970,3000],{},[751,3972,3973,3975],{},[2998,3974,3003],{},[680,3976,746],{},[596,3978,3979],{"encoding":598},"V = \\frac{\\pi \\cdot 30}{3}\\left(15^2 + 15 \\cdot 10 + 10^2\\right)\\,\\text{cm}^3 = 4750\\pi\\,\\text{cm}^3 \\approx 14\\,923\\,\\text{cm}^3",[573,3981,3983,4001,4244,4300],{"className":3982,"ariaHidden":603},[602],[573,3984,3986,3989,3992,3995,3998],{"className":3985},[607],[573,3987],{"className":3988,"style":612},[611],[573,3990,735],{"className":3991,"style":776},[616,617],[573,3993],{"className":3994,"style":702},[701],[573,3996,678],{"className":3997},[706],[573,3999],{"className":4000,"style":702},[701],[573,4002,4004,4007,4081,4084,4197,4200,4203,4235,4238,4241],{"className":4003},[607],[573,4005],{"className":4006,"style":3324},[611],[573,4008,4010,4013,4078],{"className":4009},[616],[573,4011],{"className":4012},[799,800],[573,4014,4016],{"className":4015},[739],[573,4017,4019,4070],{"className":4018},[807,808],[573,4020,4022,4067],{"className":4021},[812],[573,4023,4025,4036,4044],{"className":4024,"style":3343},[816],[573,4026,4027,4030],{"style":1698},[573,4028],{"className":4029,"style":825},[824],[573,4031,4033],{"className":4032},[616],[573,4034,746],{"className":4035},[616],[573,4037,4038,4041],{"style":841},[573,4039],{"className":4040,"style":825},[824],[573,4042],{"className":4043,"style":849},[848],[573,4045,4046,4049],{"style":1730},[573,4047],{"className":4048,"style":825},[824],[573,4050,4052,4055,4058,4061,4064],{"className":4051},[616],[573,4053,749],{"className":4054,"style":886},[616,617],[573,4056],{"className":4057,"style":776},[701],[573,4059,1006],{"className":4060},[1136],[573,4062],{"className":4063,"style":776},[701],[573,4065,3759],{"className":4066},[616],[573,4068,869],{"className":4069},[868],[573,4071,4073],{"className":4072},[812],[573,4074,4076],{"className":4075,"style":2118},[816],[573,4077],{},[573,4079],{"className":4080},[882,800],[573,4082],{"className":4083,"style":1769},[701],[573,4085,4087,4093,4096,4126,4129,4132,4135,4138,4141,4144,4147,4150,4153,4156,4159,4162,4191],{"className":4086},[2130],[573,4088,4090],{"className":4089,"style":2135},[799,2134],[573,4091,1915],{"className":4092},[2139,2140],[573,4094,743],{"className":4095},[616],[573,4097,4099,4103],{"className":4098},[616],[573,4100,4102],{"className":4101},[616],"5",[573,4104,4106],{"className":4105},[896],[573,4107,4109],{"className":4108},[807],[573,4110,4112],{"className":4111},[812],[573,4113,4115],{"className":4114,"style":2159},[816],[573,4116,4117,4120],{"style":2162},[573,4118],{"className":4119,"style":913},[824],[573,4121,4123],{"className":4122},[829,830,831,832],[573,4124,757],{"className":4125},[616,832],[573,4127],{"className":4128,"style":776},[701],[573,4130,2014],{"className":4131},[1136],[573,4133],{"className":4134,"style":776},[701],[573,4136,3803],{"className":4137},[616],[573,4139],{"className":4140,"style":776},[701],[573,4142,1006],{"className":4143},[1136],[573,4145],{"className":4146,"style":776},[701],[573,4148,3847],{"className":4149},[616],[573,4151],{"className":4152,"style":776},[701],[573,4154,2014],{"className":4155},[1136],[573,4157],{"className":4158,"style":776},[701],[573,4160,743],{"className":4161},[616],[573,4163,4165,4168],{"className":4164},[616],[573,4166,682],{"className":4167},[616],[573,4169,4171],{"className":4170},[896],[573,4172,4174],{"className":4173},[807],[573,4175,4177],{"className":4176},[812],[573,4178,4180],{"className":4179,"style":2159},[816],[573,4181,4182,4185],{"style":2162},[573,4183],{"className":4184,"style":913},[824],[573,4186,4188],{"className":4187},[829,830,831,832],[573,4189,757],{"className":4190},[616,832],[573,4192,4194],{"className":4193,"style":2135},[882,2134],[573,4195,1943],{"className":4196},[2139,2140],[573,4198],{"className":4199,"style":1769},[701],[573,4201],{"className":4202,"style":1769},[701],[573,4204,4206,4212],{"className":4205},[616],[573,4207,4209],{"className":4208},[616,3043],[573,4210,3003],{"className":4211},[616],[573,4213,4215],{"className":4214},[896],[573,4216,4218],{"className":4217},[807],[573,4219,4221],{"className":4220},[812],[573,4222,4224],{"className":4223,"style":2159},[816],[573,4225,4226,4229],{"style":2162},[573,4227],{"className":4228,"style":913},[824],[573,4230,4232],{"className":4231},[829,830,831,832],[573,4233,746],{"className":4234},[616,832],[573,4236],{"className":4237,"style":702},[701],[573,4239,678],{"className":4240},[706],[573,4242],{"className":4243,"style":702},[701],[573,4245,4247,4250,4253,4256,4259,4291,4294,4297],{"className":4246},[607],[573,4248],{"className":4249,"style":2159},[611],[573,4251,3948],{"className":4252},[616],[573,4254,749],{"className":4255,"style":886},[616,617],[573,4257],{"className":4258,"style":1769},[701],[573,4260,4262,4268],{"className":4261},[616],[573,4263,4265],{"className":4264},[616,3043],[573,4266,3003],{"className":4267},[616],[573,4269,4271],{"className":4270},[896],[573,4272,4274],{"className":4273},[807],[573,4275,4277],{"className":4276},[812],[573,4278,4280],{"className":4279,"style":2159},[816],[573,4281,4282,4285],{"style":2162},[573,4283],{"className":4284,"style":913},[824],[573,4286,4288],{"className":4287},[829,830,831,832],[573,4289,746],{"className":4290},[616,832],[573,4292],{"className":4293,"style":702},[701],[573,4295,3282],{"className":4296},[706],[573,4298],{"className":4299,"style":702},[701],[573,4301,4303,4306,4309,4312,4315,4318],{"className":4302},[607],[573,4304],{"className":4305,"style":2159},[611],[573,4307,3963],{"className":4308},[616],[573,4310],{"className":4311,"style":1769},[701],[573,4313,3968],{"className":4314},[616],[573,4316],{"className":4317,"style":1769},[701],[573,4319,4321,4327],{"className":4320},[616],[573,4322,4324],{"className":4323},[616,3043],[573,4325,3003],{"className":4326},[616],[573,4328,4330],{"className":4329},[896],[573,4331,4333],{"className":4332},[807],[573,4334,4336],{"className":4335},[812],[573,4337,4339],{"className":4338,"style":2159},[816],[573,4340,4341,4344],{"style":2162},[573,4342],{"className":4343,"style":913},[824],[573,4345,4347],{"className":4346},[829,830,831,832],[573,4348,746],{"className":4349},[616,832],[564,4351,4352,4353,4394],{},"Das sind etwa ",[573,4354,4356,4371],{"className":4355},[576],[573,4357,4359],{"className":4358},[580],[582,4360,4361],{"xmlns":584},[586,4362,4363,4368],{},[589,4364,4365],{},[680,4366,4367],{},"14,9",[596,4369,4370],{"encoding":598},"14{,}9",[573,4372,4374],{"className":4373,"ariaHidden":603},[602],[573,4375,4377,4381,4384,4390],{"className":4376},[607],[573,4378],{"className":4379,"style":4380},[611],"height:0.8389em;vertical-align:-0.1944em;",[573,4382,3963],{"className":4383},[616],[573,4385,4387],{"className":4386},[616],[573,4388,1618],{"className":4389},[1761],[573,4391,4393],{"className":4392},[616],"9"," Liter.",[559,4396,4398],{"id":4397},"typische-fehler","Typische Fehler",[656,4400,4401,4654,4756,4788],{},[659,4402,4403,4404,4582,4583,4618,4619,4653],{},"Mit dem mittleren Radius wie bei einem Zylinder rechnen: ",[573,4405,4407,4445],{"className":4406},[576],[573,4408,4410],{"className":4409},[580],[582,4411,4412],{"xmlns":584},[586,4413,4414,4442],{},[589,4415,4416,4418,4420],{},[592,4417,749],{},[592,4419,760],{},[751,4421,4422,4440],{},[589,4423,4424,4426,4438],{},[676,4425,1915],{"fence":603},[739,4427,4428,4436],{},[589,4429,4430,4432,4434],{},[592,4431,594],{},[676,4433,2014],{},[592,4435,634],{},[680,4437,757],{},[676,4439,1943],{"fence":603},[680,4441,757],{},[596,4443,4444],{"encoding":598},"\\pi h \\left(\\frac{R + r}{2}\\right)^2",[573,4446,4448],{"className":4447,"ariaHidden":603},[602],[573,4449,4451,4455,4458,4461,4464],{"className":4450},[607],[573,4452],{"className":4453,"style":4454},[611],"height:1.4263em;vertical-align:-0.35em;",[573,4456,749],{"className":4457,"style":886},[616,617],[573,4459,760],{"className":4460},[616,617],[573,4462],{"className":4463,"style":1769},[701],[573,4465,4467,4557],{"className":4466},[2130],[573,4468,4470,4476,4551],{"className":4469},[2130],[573,4471,4473],{"className":4472,"style":2135},[799,2134],[573,4474,1915],{"className":4475},[2139,2140],[573,4477,4479,4482,4548],{"className":4478},[616],[573,4480],{"className":4481},[799,800],[573,4483,4485],{"className":4484},[739],[573,4486,4488,4540],{"className":4487},[807,808],[573,4489,4491,4537],{"className":4490},[812],[573,4492,4495,4509,4517],{"className":4493,"style":4494},[816],"height:0.8723em;",[573,4496,4497,4500],{"style":820},[573,4498],{"className":4499,"style":825},[824],[573,4501,4503],{"className":4502},[829,830,831,832],[573,4504,4506],{"className":4505},[616,832],[573,4507,757],{"className":4508},[616,832],[573,4510,4511,4514],{"style":841},[573,4512],{"className":4513,"style":825},[824],[573,4515],{"className":4516,"style":849},[848],[573,4518,4519,4522],{"style":852},[573,4520],{"className":4521,"style":825},[824],[573,4523,4525],{"className":4524},[829,830,831,832],[573,4526,4528,4531,4534],{"className":4527},[616,832],[573,4529,594],{"className":4530,"style":618},[616,617,832],[573,4532,2014],{"className":4533},[1136,832],[573,4535,634],{"className":4536,"style":650},[616,617,832],[573,4538,869],{"className":4539},[868],[573,4541,4543],{"className":4542},[812],[573,4544,4546],{"className":4545,"style":876},[816],[573,4547],{},[573,4549],{"className":4550},[882,800],[573,4552,4554],{"className":4553,"style":2135},[882,2134],[573,4555,1943],{"className":4556},[2139,2140],[573,4558,4560],{"className":4559},[896],[573,4561,4563],{"className":4562},[807],[573,4564,4566],{"className":4565},[812],[573,4567,4570],{"className":4568,"style":4569},[816],"height:1.0763em;",[573,4571,4573,4576],{"style":4572},"top:-3.3252em;margin-right:0.05em;",[573,4574],{"className":4575,"style":913},[824],[573,4577,4579],{"className":4578},[829,830,831,832],[573,4580,757],{"className":4581},[616,832],". Im ersten Beispiel ergäbe das ",[573,4584,4586,4603],{"className":4585},[576],[573,4587,4589],{"className":4588},[580],[582,4590,4591],{"xmlns":584},[586,4592,4593,4600],{},[589,4594,4595,4598],{},[680,4596,4597],{},"54",[592,4599,749],{},[596,4601,4602],{"encoding":598},"54\\pi",[573,4604,4606],{"className":4605,"ariaHidden":603},[602],[573,4607,4609,4612,4615],{"className":4608},[607],[573,4610],{"className":4611,"style":716},[611],[573,4613,4597],{"className":4614},[616],[573,4616,749],{"className":4617,"style":886},[616,617]," statt ",[573,4620,4622,4638],{"className":4621},[576],[573,4623,4625],{"className":4624},[580],[582,4626,4627],{"xmlns":584},[586,4628,4629,4635],{},[589,4630,4631,4633],{},[680,4632,3269],{},[592,4634,749],{},[596,4636,4637],{"encoding":598},"56\\pi",[573,4639,4641],{"className":4640,"ariaHidden":603},[602],[573,4642,4644,4647,4650],{"className":4643},[607],[573,4645],{"className":4646,"style":716},[611],[573,4648,3269],{"className":4649},[616],[573,4651,749],{"className":4652,"style":886},[616,617],", also zu wenig.",[659,4655,4656,4657,4755],{},"Den Faktor ",[573,4658,4660,4678],{"className":4659},[576],[573,4661,4663],{"className":4662},[580],[582,4664,4665],{"xmlns":584},[586,4666,4667,4675],{},[589,4668,4669],{},[739,4670,4671,4673],{},[680,4672,743],{},[680,4674,746],{},[596,4676,4677],{"encoding":598},"\\frac{1}{3}",[573,4679,4681],{"className":4680,"ariaHidden":603},[602],[573,4682,4684,4687],{"className":4683},[607],[573,4685],{"className":4686,"style":792},[611],[573,4688,4690,4693,4752],{"className":4689},[616],[573,4691],{"className":4692},[799,800],[573,4694,4696],{"className":4695},[739],[573,4697,4699,4744],{"className":4698},[807,808],[573,4700,4702,4741],{"className":4701},[812],[573,4703,4705,4719,4727],{"className":4704,"style":817},[816],[573,4706,4707,4710],{"style":820},[573,4708],{"className":4709,"style":825},[824],[573,4711,4713],{"className":4712},[829,830,831,832],[573,4714,4716],{"className":4715},[616,832],[573,4717,746],{"className":4718},[616,832],[573,4720,4721,4724],{"style":841},[573,4722],{"className":4723,"style":825},[824],[573,4725],{"className":4726,"style":849},[848],[573,4728,4729,4732],{"style":852},[573,4730],{"className":4731,"style":825},[824],[573,4733,4735],{"className":4734},[829,830,831,832],[573,4736,4738],{"className":4737},[616,832],[573,4739,743],{"className":4740},[616,832],[573,4742,869],{"className":4743},[868],[573,4745,4747],{"className":4746},[812],[573,4748,4750],{"className":4749,"style":876},[816],[573,4751],{},[573,4753],{"className":4754},[882,800]," vergessen.",[659,4757,4758,4759,4787],{},"Die Mantellinie (schräge Seite) statt der senkrechten Höhe ",[573,4760,4762,4775],{"className":4761},[576],[573,4763,4765],{"className":4764},[580],[582,4766,4767],{"xmlns":584},[586,4768,4769,4773],{},[589,4770,4771],{},[592,4772,760],{},[596,4774,760],{"encoding":598},[573,4776,4778],{"className":4777,"ariaHidden":603},[602],[573,4779,4781,4784],{"className":4780},[607],[573,4782],{"className":4783,"style":1370},[611],[573,4785,760],{"className":4786},[616,617]," einsetzen.",[659,4789,4790],{},"Durchmesser statt Radien verwenden.",{"title":4792,"searchDepth":4793,"depth":4793,"links":4794},"",2,[4795,4796,4797,4798],{"id":561,"depth":4793,"text":562},{"id":1230,"depth":4793,"text":1231},{"id":2973,"depth":4793,"text":2974},{"id":4397,"depth":4793,"text":4398},[4800,4805,4808,4811,4814,4817,4820,4823,4826,4829],{"lhs":4801,"rhs":4802,"where":4803},"pi\u002F3*(R^2*(h*R\u002F(R - r)) - r^2*(h*r\u002F(R - r)))","pi*h\u002F3*(R^2 + R*r + r^2)",{"R":4804,"r":4793},4,{"lhs":4806,"rhs":4807},"R^3 - r^3","(R - r)*(R^2 + R*r + r^2)",{"lhs":4809,"rhs":4810},"pi*h\u002F3*(R^2 + R*0 + 0^2)","1\u002F3*pi*R^2*h",{"lhs":4812,"rhs":4813},"pi*h\u002F3*(R^2 + R*R + R^2)","pi*R^2*h",{"lhs":4815,"rhs":4816},"pi*6\u002F3*(4^2 + 4*2 + 2^2)","56*pi",{"lhs":4818,"rhs":4819},"round(56*pi, 2)","175.93",{"lhs":4821,"rhs":4822},"pi*30\u002F3*(15^2 + 15*10 + 10^2)","4750*pi",{"lhs":4824,"rhs":4825},"round(4750*pi)","14923",{"lhs":4827,"rhs":4828},"round(4750*pi\u002F1000, 1)","14.9",{"lhs":4830,"rhs":4831},"pi*6*((4 + 2)\u002F2)^2","54*pi","R \\geq r \\geq 0,\\ R > 0,\\ h > 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>R\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmi>r\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">R \\geq r \\geq 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8193em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>R\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">R > 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7224em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>h\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">h > 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":4837,"x":4838,"y":4841,"items":4844},"Kegelstumpf mit dem Radius R der Grundfläche, dem Radius r der Deckfläche und der Höhe h",[4839,4840],-2.3,2.5,[4842,4843],-0.85,2.95,[4845,4928,4934,4937,4941,4944,4947,4950,4953,4956,4961,4964,4966,4970,4974],{"type":4846,"points":4847,"fill":4926,"style":4927},"polygon",[4848,4851,4854,4857,4860,4863,4866,4869,4872,4875,4877,4879,4881,4883,4885,4887,4889,4891,4893,4895,4898,4901,4904,4907,4910,4913,4914,4916,4918,4920,4922,4924],[4849,4850],-1.8,0,[4852,4853],-1.773,-0.094,[4855,4856],-1.691,-0.185,[4858,4859],-1.559,-0.27,[4861,4862],-1.379,-0.347,[4864,4865],-1.157,-0.414,[4867,4868],-0.9,-0.468,[4870,4871],-0.616,-0.507,[4873,4874],-0.313,-0.532,[4850,4876],-0.54,[4878,4874],0.313,[4880,4871],0.616,[4882,4868],0.9,[4884,4865],1.157,[4886,4862],1.379,[4888,4859],1.559,[4890,4856],1.691,[4892,4853],1.773,[4894,4850],1.8,[4896,4897],1,2.2,[4899,4900],0.966,2.278,[4902,4903],0.866,2.35,[4905,4906],0.707,2.412,[4908,4909],0.5,2.46,[4911,4912],0.259,2.49,[4850,4840],[4915,4912],-0.259,[4917,4909],-0.5,[4919,4906],-0.707,[4921,4903],-0.866,[4923,4900],-0.966,[4925,4897],-1,true,"muted",{"type":4929,"center":4930,"rx":4894,"ry":4931,"start":4850,"end":4932,"style":4933},"ellipse",[4850,4850],0.54,180,"dashed",{"type":4929,"center":4935,"rx":4894,"ry":4931,"start":4932,"end":4936},[4850,4850],360,{"type":4938,"from":4939,"to":4940},"segment",[4849,4850],[4925,4897],{"type":4938,"from":4942,"to":4943},[4894,4850],[4896,4897],{"type":4929,"center":4945,"rx":4896,"ry":4946},[4850,4897],0.3,{"type":4938,"from":4948,"to":4949},[4850,4850],[4894,4850],{"type":4938,"from":4951,"to":4952},[4850,4897],[4896,4897],{"type":4938,"from":4954,"to":4955,"style":4933},[4850,4850],[4850,4897],{"type":4957,"at":4958,"from":4959,"to":4960},"rightAngle",[4850,4850],[4850,4897],[4894,4850],{"type":4962,"at":4963},"point",[4850,4850],{"type":4962,"at":4965},[4850,4897],{"type":4967,"at":4968,"text":594},"label",[4882,4969],-0.25,{"type":4967,"at":4971,"text":634},[4972,4973],1.3,2.45,{"type":4967,"at":4975,"text":760},[4969,4976],1.1,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 230.4 182.4\" width=\"230.4\" height=\"182.4\" role=\"img\" aria-label=\"Kegelstumpf mit dem Radius R der Grundfläche, dem Radius r der Deckfläche und der Höhe h\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-frustum-volume-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-frustum-volume-clip\">\u003Crect x=\"0\" y=\"0\" width=\"230.4\" height=\"182.4\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"24,141.6 25.3,146.11 29.23,150.48 35.57,154.56 44.21,158.26 54.86,161.47 67.2,164.06 80.83,165.94 95.38,167.14 110.4,167.52 125.42,167.14 139.97,165.94 153.6,164.06 165.94,161.47 176.59,158.26 185.23,154.56 191.57,150.48 195.5,146.11 196.8,141.6 158.4,36 156.77,32.26 151.97,28.8 144.34,25.82 134.4,23.52 122.83,22.08 110.4,21.6 97.97,22.08 86.4,23.52 76.46,25.82 68.83,28.8 64.03,32.26 62.4,36\" class=\"fig-muted fig-fill\"\u002F>\u003Cpath d=\"M 196.8 141.6 A 86.4 25.92 0 0 0 24 141.6\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 24 141.6 A 86.4 25.92 0 0 0 196.8 141.6\" class=\"fig-main\"\u002F>\u003Cline x1=\"24\" y1=\"141.6\" x2=\"62.4\" y2=\"36\" class=\"fig-main\"\u002F>\u003Cline x1=\"196.8\" y1=\"141.6\" x2=\"158.4\" y2=\"36\" class=\"fig-main\"\u002F>\u003Cellipse cx=\"110.4\" cy=\"36\" rx=\"48\" ry=\"14.4\" class=\"fig-main\"\u002F>\u003Cline x1=\"110.4\" y1=\"141.6\" x2=\"196.8\" y2=\"141.6\" class=\"fig-main\"\u002F>\u003Cline x1=\"110.4\" y1=\"36\" x2=\"158.4\" y2=\"36\" class=\"fig-main\"\u002F>\u003Cline x1=\"110.4\" y1=\"141.6\" x2=\"110.4\" y2=\"36\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 110.4 129.6 L 122.4 129.6 L 122.4 141.6\" class=\"fig-mark\"\u002F>\u003Ccircle cx=\"116.4\" cy=\"135.6\" r=\"1.5\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"110.4\" cy=\"141.6\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"110.4\" cy=\"36\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"153.6\" y=\"153.6\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">R\u003C\u002Ftext>\u003Ctext x=\"172.8\" y=\"24\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003C\u002Ftext>\u003Ctext x=\"98.4\" y=\"88.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">h\u003C\u002Ftext>\u003C\u002Fsvg>","frustum-volume","V = \\frac{\\pi h}{3} \\left(R^2 + R r + r^2\\right)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>π\u003C\u002Fmi>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmi>R\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>R\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V = \\frac{\\pi h}{3} \\left(R^2 + R r + r^2\\right)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0574em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-kegelstumpf",[],[4986,4987,4988,4989],"cone-volume","cylinder-volume","cone-surface","intercept-theorem",{"title":548,"description":4792},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-kegelstumpf","Ein Kegelstumpf mit den Radien R und r und der Höhe h hat das Volumen πh\u002F3 · (R² + Rr + r²).",[4994,4995,4996,4997],"volumen","kegelstumpf","kegel","körper",[4999,5002,5005,5008,5011],{"symbol":735,"meaning":5000,"symbolHtml":5001},"Volumen des Kegelstumpfs","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":760,"meaning":5003,"symbolHtml":5004},"Höhe, der senkrechte Abstand von Grund- und Deckfläche","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">h\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":594,"meaning":5006,"symbolHtml":5007},"Radius der größeren Kreisfläche","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>R\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">R\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":634,"meaning":5009,"symbolHtml":5010},"Radius der kleineren Kreisfläche","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>r\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5012,"meaning":5013,"symbolHtml":5014},"\\pi","Kreiszahl, etwa 3,14159","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>π\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\pi\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","JqL9AhjyH34Nf8malnNgVPvuSljoV8MTpfllyk_en-A",[5017,5020,5023,5026],{"stem":5018,"title":5019,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kegel","Oberfläche eines Kegels",{"stem":5021,"title":5022,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fstrahlensatz","Strahlensatz",{"stem":5024,"title":5025,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-kegel","Volumen eines Kegels",{"stem":5027,"title":5028,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-zylinder","Volumen eines Zylinders",1793824270710]