[{"data":1,"prerenderedAt":2562},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kegelstumpf":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kegelstumpf":2552},[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":554,"category":247,"checks":2350,"conditions":2365,"conditionsHtml":2366,"deprecated":2367,"description":2343,"extension":2368,"figure":2369,"figureCaption":2370,"figureHtml":2514,"formulaId":2515,"latex":2516,"latexHtml":2517,"level":2518,"meta":2519,"navigation":2459,"path":2520,"redirectFrom":2521,"related":2522,"seo":2526,"stem":2527,"subject":591,"summary":2528,"tags":2529,"variables":2535,"__hash__":2551},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kegelstumpf.md","Oberfläche eines Kegelstumpfs",[550,551,552,553],"Kegelstumpf Oberfläche","Mantelfläche Kegelstumpf","Oberfläche Eimer","Mantellinie Kegelstumpf",{"type":555,"value":556,"toc":2342},"minimark",[557,562,571,574,877,997,1000,1004,1163,1362,1366,1569,1805,1808,2050,2166,2170],[558,559,561],"h2",{"id":560},"erklärung","Erklärung",[563,564,565,566,570],"p",{},"Ein ",[567,568,569],"strong",{},"Kegelstumpf"," entsteht, wenn man von einem Kegel parallel zur Grundfläche die Spitze abschneidet. Ein Eimer oder ein Lampenschirm hat diese Form.",[563,572,573],{},"Seine Oberfläche besteht aus drei Teilen:",[575,576,577,681,750],"ul",{},[578,579,580,581,680],"li",{},"dem Grundkreis ",[582,583,586,619],"span",{"className":584},[585],"katex",[582,587,590],{"className":588},[589],"katex-mathml",[591,592,594],"math",{"xmlns":593},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[595,596,597,614],"semantics",{},[598,599,600,604],"mrow",{},[601,602,603],"mi",{},"π",[605,606,607,610],"msup",{},[601,608,609],{},"R",[611,612,613],"mn",{},"2",[615,616,618],"annotation",{"encoding":617},"application\u002Fx-tex","\\pi R^2",[582,620,624],{"className":621,"ariaHidden":623},[622],"katex-html","true",[582,625,628,633,639],{"className":626},[627],"base",[582,629],{"className":630,"style":632},[631],"strut","height:0.8141em;",[582,634,603],{"className":635,"style":638},[636,637],"mord","mathnormal","margin-right:0.0359em;",[582,640,642,646],{"className":641},[636],[582,643,609],{"className":644,"style":645},[636,637],"margin-right:0.0077em;",[582,647,650],{"className":648},[649],"msupsub",[582,651,654],{"className":652},[653],"vlist-t",[582,655,658],{"className":656},[657],"vlist-r",[582,659,662],{"className":660,"style":632},[661],"vlist",[582,663,665,670],{"style":664},"top:-3.063em;margin-right:0.05em;",[582,666],{"className":667,"style":669},[668],"pstrut","height:2.7em;",[582,671,677],{"className":672},[673,674,675,676],"sizing","reset-size6","size3","mtight",[582,678,613],{"className":679},[636,676],",",[578,682,683,684,680],{},"dem Deckkreis ",[582,685,687,708],{"className":686},[585],[582,688,690],{"className":689},[589],[591,691,692],{"xmlns":593},[595,693,694,705],{},[598,695,696,698],{},[601,697,603],{},[605,699,700,703],{},[601,701,702],{},"r",[611,704,613],{},[615,706,707],{"encoding":617},"\\pi r^2",[582,709,711],{"className":710,"ariaHidden":623},[622],[582,712,714,717,720],{"className":713},[627],[582,715],{"className":716,"style":632},[631],[582,718,603],{"className":719,"style":638},[636,637],[582,721,723,727],{"className":722},[636],[582,724,702],{"className":725,"style":726},[636,637],"margin-right:0.0278em;",[582,728,730],{"className":729},[649],[582,731,733],{"className":732},[653],[582,734,736],{"className":735},[657],[582,737,739],{"className":738,"style":632},[661],[582,740,741,744],{"style":664},[582,742],{"className":743,"style":669},[668],[582,745,747],{"className":746},[673,674,675,676],[582,748,613],{"className":749},[636,676],[578,751,752,753,756,757,876],{},"dem ",[567,754,755],{},"Mantel"," ",[582,758,760,802],{"className":759},[585],[582,761,763],{"className":762},[589],[591,764,765],{"xmlns":593},[595,766,767,799],{},[598,768,769,772,776,778,782,784,787,789,792,796],{},[601,770,771],{},"M",[773,774,775],"mo",{},"=",[601,777,603],{},[773,779,781],{"stretchy":780},"false","(",[601,783,609],{},[773,785,786],{},"+",[601,788,702],{},[773,790,791],{"stretchy":780},")",[793,794,795],"mtext",{}," ",[601,797,798],{},"s",[615,800,801],{"encoding":617},"M = \\pi (R + r)\\, s",[582,803,805,828,856],{"className":804,"ariaHidden":623},[622],[582,806,808,812,816,821,825],{"className":807},[627],[582,809],{"className":810,"style":811},[631],"height:0.6833em;",[582,813,771],{"className":814,"style":815},[636,637],"margin-right:0.109em;",[582,817],{"className":818,"style":820},[819],"mspace","margin-right:0.2778em;",[582,822,775],{"className":823},[824],"mrel",[582,826],{"className":827,"style":820},[819],[582,829,831,835,838,842,845,849,853],{"className":830},[627],[582,832],{"className":833,"style":834},[631],"height:1em;vertical-align:-0.25em;",[582,836,603],{"className":837,"style":638},[636,637],[582,839,781],{"className":840},[841],"mopen",[582,843,609],{"className":844,"style":645},[636,637],[582,846],{"className":847,"style":848},[819],"margin-right:0.2222em;",[582,850,786],{"className":851},[852],"mbin",[582,854],{"className":855,"style":848},[819],[582,857,859,862,865,869,873],{"className":858},[627],[582,860],{"className":861,"style":834},[631],[582,863,702],{"className":864,"style":726},[636,637],[582,866,791],{"className":867},[868],"mclose",[582,870],{"className":871,"style":872},[819],"margin-right:0.1667em;",[582,874,798],{"className":875},[636,637],".",[563,878,879,880,756,883,912,913,943,944,876],{},"Die ",[567,881,882],{},"Mantellinie",[582,884,886,899],{"className":885},[585],[582,887,889],{"className":888},[589],[591,890,891],{"xmlns":593},[595,892,893,897],{},[598,894,895],{},[601,896,798],{},[615,898,798],{"encoding":617},[582,900,902],{"className":901,"ariaHidden":623},[622],[582,903,905,909],{"className":904},[627],[582,906],{"className":907,"style":908},[631],"height:0.4306em;",[582,910,798],{"className":911},[636,637]," ist die schräge Strecke vom Rand des Grundkreises zum Rand des Deckkreises. Man berechnet sie mit dem Satz des Pythagoras im Trapez-Querschnitt: Die Katheten sind die Höhe ",[582,914,916,930],{"className":915},[585],[582,917,919],{"className":918},[589],[591,920,921],{"xmlns":593},[595,922,923,928],{},[598,924,925],{},[601,926,927],{},"h",[615,929,927],{"encoding":617},[582,931,933],{"className":932,"ariaHidden":623},[622],[582,934,936,940],{"className":935},[627],[582,937],{"className":938,"style":939},[631],"height:0.6944em;",[582,941,927],{"className":942},[636,637]," und der Radienunterschied ",[582,945,947,966],{"className":946},[585],[582,948,950],{"className":949},[589],[591,951,952],{"xmlns":593},[595,953,954,963],{},[598,955,956,958,961],{},[601,957,609],{},[773,959,960],{},"−",[601,962,702],{},[615,964,965],{"encoding":617},"R - r",[582,967,969,988],{"className":968,"ariaHidden":623},[622],[582,970,972,976,979,982,985],{"className":971},[627],[582,973],{"className":974,"style":975},[631],"height:0.7667em;vertical-align:-0.0833em;",[582,977,609],{"className":978,"style":645},[636,637],[582,980],{"className":981,"style":848},[819],[582,983,960],{"className":984},[852],[582,986],{"className":987,"style":848},[819],[582,989,991,994],{"className":990},[627],[582,992],{"className":993,"style":908},[631],[582,995,702],{"className":996,"style":726},[636,637],[563,998,999],{},"Für einen offenen Behälter wie einen Eimer lässt man den Deckkreis weg.",[558,1001,1003],{"id":1002},"herleitung","Herleitung",[563,1005,1006,1007,1162],{},"Der Mantel ist der Mantel des ganzen Kegels minus der Mantel der abgeschnittenen Spitze. Mit der Mantellinie ",[582,1008,1010,1044],{"className":1009},[585],[582,1011,1013],{"className":1012},[589],[591,1014,1015],{"xmlns":593},[595,1016,1017,1041],{},[598,1018,1019,1022,1024],{},[601,1020,1021],{},"S",[773,1023,775],{},[1025,1026,1027,1033],"mfrac",{},[598,1028,1029,1031],{},[601,1030,798],{},[601,1032,609],{},[598,1034,1035,1037,1039],{},[601,1036,609],{},[773,1038,960],{},[601,1040,702],{},[615,1042,1043],{"encoding":617},"S = \\frac{sR}{R - r}",[582,1045,1047,1066],{"className":1046,"ariaHidden":623},[622],[582,1048,1050,1053,1057,1060,1063],{"className":1049},[627],[582,1051],{"className":1052,"style":811},[631],[582,1054,1021],{"className":1055,"style":1056},[636,637],"margin-right:0.0576em;",[582,1058],{"className":1059,"style":820},[819],[582,1061,775],{"className":1062},[824],[582,1064],{"className":1065,"style":820},[819],[582,1067,1069,1073],{"className":1068},[627],[582,1070],{"className":1071,"style":1072},[631],"height:1.2757em;vertical-align:-0.4033em;",[582,1074,1076,1080,1159],{"className":1075},[636],[582,1077],{"className":1078},[841,1079],"nulldelimiter",[582,1081,1083],{"className":1082},[1025],[582,1084,1087,1150],{"className":1085},[653,1086],"vlist-t2",[582,1088,1090,1145],{"className":1089},[657],[582,1091,1094,1116,1127],{"className":1092,"style":1093},[661],"height:0.8723em;",[582,1095,1097,1101],{"style":1096},"top:-2.655em;",[582,1098],{"className":1099,"style":1100},[668],"height:3em;",[582,1102,1104],{"className":1103},[673,674,675,676],[582,1105,1107,1110,1113],{"className":1106},[636,676],[582,1108,609],{"className":1109,"style":645},[636,637,676],[582,1111,960],{"className":1112},[852,676],[582,1114,702],{"className":1115,"style":726},[636,637,676],[582,1117,1119,1122],{"style":1118},"top:-3.23em;",[582,1120],{"className":1121,"style":1100},[668],[582,1123],{"className":1124,"style":1126},[1125],"frac-line","border-bottom-width:0.04em;",[582,1128,1130,1133],{"style":1129},"top:-3.394em;",[582,1131],{"className":1132,"style":1100},[668],[582,1134,1136],{"className":1135},[673,674,675,676],[582,1137,1139,1142],{"className":1138},[636,676],[582,1140,798],{"className":1141},[636,637,676],[582,1143,609],{"className":1144,"style":645},[636,637,676],[582,1146,1149],{"className":1147},[1148],"vlist-s","​",[582,1151,1153],{"className":1152},[657],[582,1154,1157],{"className":1155,"style":1156},[661],"height:0.4033em;",[582,1158],{},[582,1160],{"className":1161},[868,1079]," des ganzen Kegels (Strahlensatz) ergibt sich",[582,1164,1167],{"className":1165},[1166],"katex-display",[582,1168,1170,1227],{"className":1169},[585],[582,1171,1173],{"className":1172},[589],[591,1174,1176],{"xmlns":593,"display":1175},"block",[595,1177,1178,1224],{},[598,1179,1180,1182,1184,1186,1188,1190,1192,1194,1196,1198,1200,1202,1204,1206,1208,1210,1212,1214,1216,1218,1220,1222],{},[601,1181,771],{},[773,1183,775],{},[601,1185,603],{},[601,1187,609],{},[601,1189,1021],{},[773,1191,960],{},[601,1193,603],{},[601,1195,702],{},[773,1197,781],{"stretchy":780},[601,1199,1021],{},[773,1201,960],{},[601,1203,798],{},[773,1205,791],{"stretchy":780},[773,1207,775],{},[601,1209,603],{},[773,1211,781],{"stretchy":780},[601,1213,609],{},[773,1215,786],{},[601,1217,702],{},[773,1219,791],{"stretchy":780},[793,1221,795],{},[601,1223,798],{},[615,1225,1226],{"encoding":617},"M = \\pi R S - \\pi r (S - s) = \\pi (R + r)\\, s",[582,1228,1230,1248,1272,1299,1320,1344],{"className":1229,"ariaHidden":623},[622],[582,1231,1233,1236,1239,1242,1245],{"className":1232},[627],[582,1234],{"className":1235,"style":811},[631],[582,1237,771],{"className":1238,"style":815},[636,637],[582,1240],{"className":1241,"style":820},[819],[582,1243,775],{"className":1244},[824],[582,1246],{"className":1247,"style":820},[819],[582,1249,1251,1254,1257,1260,1263,1266,1269],{"className":1250},[627],[582,1252],{"className":1253,"style":975},[631],[582,1255,603],{"className":1256,"style":638},[636,637],[582,1258,609],{"className":1259,"style":645},[636,637],[582,1261,1021],{"className":1262,"style":1056},[636,637],[582,1264],{"className":1265,"style":848},[819],[582,1267,960],{"className":1268},[852],[582,1270],{"className":1271,"style":848},[819],[582,1273,1275,1278,1281,1284,1287,1290,1293,1296],{"className":1274},[627],[582,1276],{"className":1277,"style":834},[631],[582,1279,603],{"className":1280,"style":638},[636,637],[582,1282,702],{"className":1283,"style":726},[636,637],[582,1285,781],{"className":1286},[841],[582,1288,1021],{"className":1289,"style":1056},[636,637],[582,1291],{"className":1292,"style":848},[819],[582,1294,960],{"className":1295},[852],[582,1297],{"className":1298,"style":848},[819],[582,1300,1302,1305,1308,1311,1314,1317],{"className":1301},[627],[582,1303],{"className":1304,"style":834},[631],[582,1306,798],{"className":1307},[636,637],[582,1309,791],{"className":1310},[868],[582,1312],{"className":1313,"style":820},[819],[582,1315,775],{"className":1316},[824],[582,1318],{"className":1319,"style":820},[819],[582,1321,1323,1326,1329,1332,1335,1338,1341],{"className":1322},[627],[582,1324],{"className":1325,"style":834},[631],[582,1327,603],{"className":1328,"style":638},[636,637],[582,1330,781],{"className":1331},[841],[582,1333,609],{"className":1334,"style":645},[636,637],[582,1336],{"className":1337,"style":848},[819],[582,1339,786],{"className":1340},[852],[582,1342],{"className":1343,"style":848},[819],[582,1345,1347,1350,1353,1356,1359],{"className":1346},[627],[582,1348],{"className":1349,"style":834},[631],[582,1351,702],{"className":1352,"style":726},[636,637],[582,1354,791],{"className":1355},[868],[582,1357],{"className":1358,"style":872},[819],[582,1360,798],{"className":1361},[636,637],[558,1363,1365],{"id":1364},"beispiele","Beispiele",[563,1367,1368,1369,1437,1438,1502,1503,1568],{},"Ein Kegelstumpf hat ",[582,1370,1372,1396],{"className":1371},[585],[582,1373,1375],{"className":1374},[589],[591,1376,1377],{"xmlns":593},[595,1378,1379,1393],{},[598,1380,1381,1383,1385,1388,1390],{},[601,1382,609],{},[773,1384,775],{},[611,1386,1387],{},"5",[793,1389,795],{},[793,1391,1392],{},"cm",[615,1394,1395],{"encoding":617},"R = 5\\,\\text{cm}",[582,1397,1399,1417],{"className":1398,"ariaHidden":623},[622],[582,1400,1402,1405,1408,1411,1414],{"className":1401},[627],[582,1403],{"className":1404,"style":811},[631],[582,1406,609],{"className":1407,"style":645},[636,637],[582,1409],{"className":1410,"style":820},[819],[582,1412,775],{"className":1413},[824],[582,1415],{"className":1416,"style":820},[819],[582,1418,1420,1424,1427,1430],{"className":1419},[627],[582,1421],{"className":1422,"style":1423},[631],"height:0.6444em;",[582,1425,1387],{"className":1426},[636],[582,1428],{"className":1429,"style":872},[819],[582,1431,1434],{"className":1432},[636,1433],"text",[582,1435,1392],{"className":1436},[636],", ",[582,1439,1441,1463],{"className":1440},[585],[582,1442,1444],{"className":1443},[589],[591,1445,1446],{"xmlns":593},[595,1447,1448,1460],{},[598,1449,1450,1452,1454,1456,1458],{},[601,1451,702],{},[773,1453,775],{},[611,1455,613],{},[793,1457,795],{},[793,1459,1392],{},[615,1461,1462],{"encoding":617},"r = 2\\,\\text{cm}",[582,1464,1466,1484],{"className":1465,"ariaHidden":623},[622],[582,1467,1469,1472,1475,1478,1481],{"className":1468},[627],[582,1470],{"className":1471,"style":908},[631],[582,1473,702],{"className":1474,"style":726},[636,637],[582,1476],{"className":1477,"style":820},[819],[582,1479,775],{"className":1480},[824],[582,1482],{"className":1483,"style":820},[819],[582,1485,1487,1490,1493,1496],{"className":1486},[627],[582,1488],{"className":1489,"style":1423},[631],[582,1491,613],{"className":1492},[636],[582,1494],{"className":1495,"style":872},[819],[582,1497,1499],{"className":1498},[636,1433],[582,1500,1392],{"className":1501},[636]," und ",[582,1504,1506,1529],{"className":1505},[585],[582,1507,1509],{"className":1508},[589],[591,1510,1511],{"xmlns":593},[595,1512,1513,1526],{},[598,1514,1515,1517,1519,1522,1524],{},[601,1516,927],{},[773,1518,775],{},[611,1520,1521],{},"4",[793,1523,795],{},[793,1525,1392],{},[615,1527,1528],{"encoding":617},"h = 4\\,\\text{cm}",[582,1530,1532,1550],{"className":1531,"ariaHidden":623},[622],[582,1533,1535,1538,1541,1544,1547],{"className":1534},[627],[582,1536],{"className":1537,"style":939},[631],[582,1539,927],{"className":1540},[636,637],[582,1542],{"className":1543,"style":820},[819],[582,1545,775],{"className":1546},[824],[582,1548],{"className":1549,"style":820},[819],[582,1551,1553,1556,1559,1562],{"className":1552},[627],[582,1554],{"className":1555,"style":1423},[631],[582,1557,1521],{"className":1558},[636],[582,1560],{"className":1561,"style":872},[819],[582,1563,1565],{"className":1564},[636,1433],[582,1566,1392],{"className":1567},[636],". Zuerst die Mantellinie:",[582,1570,1572],{"className":1571},[1166],[582,1573,1575,1619],{"className":1574},[585],[582,1576,1578],{"className":1577},[589],[591,1579,1580],{"xmlns":593,"display":1175},[595,1581,1582,1616],{},[598,1583,1584,1586,1588,1608,1610,1612,1614],{},[601,1585,798],{},[773,1587,775],{},[1589,1590,1591],"msqrt",{},[598,1592,1593,1600,1602],{},[605,1594,1595,1598],{},[611,1596,1597],{},"3",[611,1599,613],{},[773,1601,786],{},[605,1603,1604,1606],{},[611,1605,1521],{},[611,1607,613],{},[773,1609,775],{},[611,1611,1387],{},[793,1613,795],{},[793,1615,1392],{},[615,1617,1618],{"encoding":617},"s = \\sqrt{3^2 + 4^2} = 5\\,\\text{cm}",[582,1620,1622,1640,1787],{"className":1621,"ariaHidden":623},[622],[582,1623,1625,1628,1631,1634,1637],{"className":1624},[627],[582,1626],{"className":1627,"style":908},[631],[582,1629,798],{"className":1630},[636,637],[582,1632],{"className":1633,"style":820},[819],[582,1635,775],{"className":1636},[824],[582,1638],{"className":1639,"style":820},[819],[582,1641,1643,1647,1778,1781,1784],{"className":1642},[627],[582,1644],{"className":1645,"style":1646},[631],"height:1.24em;vertical-align:-0.1777em;",[582,1648,1651],{"className":1649},[636,1650],"sqrt",[582,1652,1654,1769],{"className":1653},[653,1086],[582,1655,1657,1766],{"className":1656},[657],[582,1658,1661,1743],{"className":1659,"style":1660},[661],"height:1.0623em;",[582,1662,1666,1670],{"className":1663,"style":1665},[1664],"svg-align","top:-3.2em;",[582,1667],{"className":1668,"style":1669},[668],"height:3.2em;",[582,1671,1674,1705,1708,1711,1714],{"className":1672,"style":1673},[636],"padding-left:1em;",[582,1675,1677,1680],{"className":1676},[636],[582,1678,1597],{"className":1679},[636],[582,1681,1683],{"className":1682},[649],[582,1684,1686],{"className":1685},[653],[582,1687,1689],{"className":1688},[657],[582,1690,1693],{"className":1691,"style":1692},[661],"height:0.7401em;",[582,1694,1696,1699],{"style":1695},"top:-2.989em;margin-right:0.05em;",[582,1697],{"className":1698,"style":669},[668],[582,1700,1702],{"className":1701},[673,674,675,676],[582,1703,613],{"className":1704},[636,676],[582,1706],{"className":1707,"style":848},[819],[582,1709,786],{"className":1710},[852],[582,1712],{"className":1713,"style":848},[819],[582,1715,1717,1720],{"className":1716},[636],[582,1718,1521],{"className":1719},[636],[582,1721,1723],{"className":1722},[649],[582,1724,1726],{"className":1725},[653],[582,1727,1729],{"className":1728},[657],[582,1730,1732],{"className":1731,"style":1692},[661],[582,1733,1734,1737],{"style":1695},[582,1735],{"className":1736,"style":669},[668],[582,1738,1740],{"className":1739},[673,674,675,676],[582,1741,613],{"className":1742},[636,676],[582,1744,1746,1749],{"style":1745},"top:-3.0223em;",[582,1747],{"className":1748,"style":1669},[668],[582,1750,1754],{"className":1751,"style":1753},[1752],"hide-tail","min-width:1.02em;height:1.28em;",[1755,1756,1762],"svg",{"xmlns":1757,"width":1758,"height":1759,"viewBox":1760,"preserveAspectRatio":1761},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.28em","0 0 400000 1296","xMinYMin slice",[1763,1764],"path",{"d":1765},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[582,1767,1149],{"className":1768},[1148],[582,1770,1772],{"className":1771},[657],[582,1773,1776],{"className":1774,"style":1775},[661],"height:0.1777em;",[582,1777],{},[582,1779],{"className":1780,"style":820},[819],[582,1782,775],{"className":1783},[824],[582,1785],{"className":1786,"style":820},[819],[582,1788,1790,1793,1796,1799],{"className":1789},[627],[582,1791],{"className":1792,"style":1423},[631],[582,1794,1387],{"className":1795},[636],[582,1797],{"className":1798,"style":872},[819],[582,1800,1802],{"className":1801},[636,1433],[582,1803,1392],{"className":1804},[636],[563,1806,1807],{},"Dann die Oberfläche:",[582,1809,1811],{"className":1810},[1166],[582,1812,1814,1877],{"className":1813},[585],[582,1815,1817],{"className":1816},[589],[591,1818,1819],{"xmlns":593,"display":1175},[595,1820,1821,1874],{},[598,1822,1823,1826,1828,1830,1853,1855,1858,1860,1863,1866,1868],{},[601,1824,1825],{},"O",[773,1827,775],{},[601,1829,603],{},[598,1831,1832,1834,1837,1839,1841,1843,1846,1849,1851],{},[773,1833,781],{"fence":623},[611,1835,1836],{},"25",[773,1838,786],{},[611,1840,1521],{},[773,1842,786],{},[611,1844,1845],{},"7",[773,1847,1848],{},"⋅",[611,1850,1387],{},[773,1852,791],{"fence":623},[773,1854,775],{},[611,1856,1857],{},"64",[601,1859,603],{},[773,1861,1862],{},"≈",[611,1864,1865],{},"201,06",[793,1867,795],{},[605,1869,1870,1872],{},[793,1871,1392],{},[611,1873,613],{},[615,1875,1876],{"encoding":617},"O = \\pi \\left(25 + 4 + 7 \\cdot 5\\right) = 64\\pi \\approx 201{,}06\\,\\text{cm}^2",[582,1878,1880,1898,1970,1991],{"className":1879,"ariaHidden":623},[622],[582,1881,1883,1886,1889,1892,1895],{"className":1882},[627],[582,1884],{"className":1885,"style":811},[631],[582,1887,1825],{"className":1888,"style":726},[636,637],[582,1890],{"className":1891,"style":820},[819],[582,1893,775],{"className":1894},[824],[582,1896],{"className":1897,"style":820},[819],[582,1899,1901,1904,1907,1910,1961,1964,1967],{"className":1900},[627],[582,1902],{"className":1903,"style":834},[631],[582,1905,603],{"className":1906,"style":638},[636,637],[582,1908],{"className":1909,"style":872},[819],[582,1911,1914,1919,1922,1925,1928,1931,1934,1937,1940,1943,1946,1949,1952,1955,1958],{"className":1912},[1913],"minner",[582,1915,781],{"className":1916,"style":1918},[841,1917],"delimcenter","top:0em;",[582,1920,1836],{"className":1921},[636],[582,1923],{"className":1924,"style":848},[819],[582,1926,786],{"className":1927},[852],[582,1929],{"className":1930,"style":848},[819],[582,1932,1521],{"className":1933},[636],[582,1935],{"className":1936,"style":848},[819],[582,1938,786],{"className":1939},[852],[582,1941],{"className":1942,"style":848},[819],[582,1944,1845],{"className":1945},[636],[582,1947],{"className":1948,"style":848},[819],[582,1950,1848],{"className":1951},[852],[582,1953],{"className":1954,"style":848},[819],[582,1956,1387],{"className":1957},[636],[582,1959,791],{"className":1960,"style":1918},[868,1917],[582,1962],{"className":1963,"style":820},[819],[582,1965,775],{"className":1966},[824],[582,1968],{"className":1969,"style":820},[819],[582,1971,1973,1976,1979,1982,1985,1988],{"className":1972},[627],[582,1974],{"className":1975,"style":1423},[631],[582,1977,1857],{"className":1978},[636],[582,1980,603],{"className":1981,"style":638},[636,637],[582,1983],{"className":1984,"style":820},[819],[582,1986,1862],{"className":1987},[824],[582,1989],{"className":1990,"style":820},[819],[582,1992,1994,1998,2002,2009,2013,2016],{"className":1993},[627],[582,1995],{"className":1996,"style":1997},[631],"height:1.0585em;vertical-align:-0.1944em;",[582,1999,2001],{"className":2000},[636],"201",[582,2003,2005],{"className":2004},[636],[582,2006,680],{"className":2007},[2008],"mpunct",[582,2010,2012],{"className":2011},[636],"06",[582,2014],{"className":2015,"style":872},[819],[582,2017,2019,2025],{"className":2018},[636],[582,2020,2022],{"className":2021},[636,1433],[582,2023,1392],{"className":2024},[636],[582,2026,2028],{"className":2027},[649],[582,2029,2031],{"className":2030},[653],[582,2032,2034],{"className":2033},[657],[582,2035,2038],{"className":2036,"style":2037},[661],"height:0.8641em;",[582,2039,2041,2044],{"style":2040},"top:-3.113em;margin-right:0.05em;",[582,2042],{"className":2043,"style":669},[668],[582,2045,2047],{"className":2046},[673,674,675,676],[582,2048,613],{"className":2049},[636,676],[563,2051,2052,2053,876],{},"Der Mantel allein ist ",[582,2054,2056,2086],{"className":2055},[585],[582,2057,2059],{"className":2058},[589],[591,2060,2061],{"xmlns":593},[595,2062,2063,2083],{},[598,2064,2065,2068,2070,2072,2075,2077],{},[611,2066,2067],{},"35",[601,2069,603],{},[773,2071,1862],{},[611,2073,2074],{},"109,96",[793,2076,795],{},[605,2078,2079,2081],{},[793,2080,1392],{},[611,2082,613],{},[615,2084,2085],{"encoding":617},"35\\pi \\approx 109{,}96\\,\\text{cm}^2",[582,2087,2089,2110],{"className":2088,"ariaHidden":623},[622],[582,2090,2092,2095,2098,2101,2104,2107],{"className":2091},[627],[582,2093],{"className":2094,"style":1423},[631],[582,2096,2067],{"className":2097},[636],[582,2099,603],{"className":2100,"style":638},[636,637],[582,2102],{"className":2103,"style":820},[819],[582,2105,1862],{"className":2106},[824],[582,2108],{"className":2109,"style":820},[819],[582,2111,2113,2117,2121,2127,2131,2134],{"className":2112},[627],[582,2114],{"className":2115,"style":2116},[631],"height:1.0085em;vertical-align:-0.1944em;",[582,2118,2120],{"className":2119},[636],"109",[582,2122,2124],{"className":2123},[636],[582,2125,680],{"className":2126},[2008],[582,2128,2130],{"className":2129},[636],"96",[582,2132],{"className":2133,"style":872},[819],[582,2135,2137,2143],{"className":2136},[636],[582,2138,2140],{"className":2139},[636,1433],[582,2141,1392],{"className":2142},[636],[582,2144,2146],{"className":2145},[649],[582,2147,2149],{"className":2148},[653],[582,2150,2152],{"className":2151},[657],[582,2153,2155],{"className":2154,"style":632},[661],[582,2156,2157,2160],{"style":664},[582,2158],{"className":2159,"style":669},[668],[582,2161,2163],{"className":2162},[673,674,675,676],[582,2164,613],{"className":2165},[636,676],[558,2167,2169],{"id":2168},"typische-fehler","Typische Fehler",[575,2171,2172,2233,2339],{},[578,2173,2174,2175,2203,2204,2232],{},"Die Höhe ",[582,2176,2178,2191],{"className":2177},[585],[582,2179,2181],{"className":2180},[589],[591,2182,2183],{"xmlns":593},[595,2184,2185,2189],{},[598,2186,2187],{},[601,2188,927],{},[615,2190,927],{"encoding":617},[582,2192,2194],{"className":2193,"ariaHidden":623},[622],[582,2195,2197,2200],{"className":2196},[627],[582,2198],{"className":2199,"style":939},[631],[582,2201,927],{"className":2202},[636,637]," statt der Mantellinie ",[582,2205,2207,2220],{"className":2206},[585],[582,2208,2210],{"className":2209},[589],[591,2211,2212],{"xmlns":593},[595,2213,2214,2218],{},[598,2215,2216],{},[601,2217,798],{},[615,2219,798],{"encoding":617},[582,2221,2223],{"className":2222,"ariaHidden":623},[622],[582,2224,2226,2229],{"className":2225},[627],[582,2227],{"className":2228,"style":908},[631],[582,2230,798],{"className":2231},[636,637]," in die Mantelformel einsetzen.",[578,2234,2235,2236,2287,2288,2338],{},"Bei der Mantellinie ",[582,2237,2239,2257],{"className":2238},[585],[582,2240,2242],{"className":2241},[589],[591,2243,2244],{"xmlns":593},[595,2245,2246,2254],{},[598,2247,2248,2250,2252],{},[601,2249,609],{},[773,2251,786],{},[601,2253,702],{},[615,2255,2256],{"encoding":617},"R + r",[582,2258,2260,2278],{"className":2259,"ariaHidden":623},[622],[582,2261,2263,2266,2269,2272,2275],{"className":2262},[627],[582,2264],{"className":2265,"style":975},[631],[582,2267,609],{"className":2268,"style":645},[636,637],[582,2270],{"className":2271,"style":848},[819],[582,2273,786],{"className":2274},[852],[582,2276],{"className":2277,"style":848},[819],[582,2279,2281,2284],{"className":2280},[627],[582,2282],{"className":2283,"style":908},[631],[582,2285,702],{"className":2286,"style":726},[636,637]," statt ",[582,2289,2291,2308],{"className":2290},[585],[582,2292,2294],{"className":2293},[589],[591,2295,2296],{"xmlns":593},[595,2297,2298,2306],{},[598,2299,2300,2302,2304],{},[601,2301,609],{},[773,2303,960],{},[601,2305,702],{},[615,2307,965],{"encoding":617},[582,2309,2311,2329],{"className":2310,"ariaHidden":623},[622],[582,2312,2314,2317,2320,2323,2326],{"className":2313},[627],[582,2315],{"className":2316,"style":975},[631],[582,2318,609],{"className":2319,"style":645},[636,637],[582,2321],{"className":2322,"style":848},[819],[582,2324,960],{"className":2325},[852],[582,2327],{"className":2328,"style":848},[819],[582,2330,2332,2335],{"className":2331},[627],[582,2333],{"className":2334,"style":908},[631],[582,2336,702],{"className":2337,"style":726},[636,637]," als Kathete nehmen.",[578,2340,2341],{},"Bei offenen Gefäßen trotzdem den Deckel mitrechnen, oder bei geschlossenen Körpern einen Kreis vergessen.",{"title":2343,"searchDepth":2344,"depth":2344,"links":2345},"",2,[2346,2347,2348,2349],{"id":560,"depth":2344,"text":561},{"id":1002,"depth":2344,"text":1003},{"id":1364,"depth":2344,"text":1365},{"id":2168,"depth":2344,"text":2169},[2351,2354,2356,2359,2362],{"lhs":2352,"rhs":2353},"pi*(R + r)*s","pi*R*(s*R\u002F(R - r)) - pi*r*(s*R\u002F(R - r) - s)",{"lhs":2355,"rhs":1387},"sqrt((5 - 2)^2 + 4^2)",{"lhs":2357,"rhs":2358},"pi*(5^2 + 2^2 + (5 + 2)*5)","64*pi",{"lhs":2360,"rhs":2361},"round(64*pi, 2)","201.06",{"lhs":2363,"rhs":2364},"round(pi*(5 + 2)*5, 2)","109.96","R > r > 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>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">R > 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:0.5782em;vertical-align:-0.0391em;\">\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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":2370,"x":2371,"y":2374,"items":2377},"Kegelstumpf mit den Radien R und r, der Höhe h und der Mantellinie s",[2372,2373],-2.3,2.5,[2375,2376],-0.85,2.95,[2378,2461,2467,2470,2474,2477,2480,2483,2486,2489,2494,2497,2499,2503,2507,2510],{"type":2379,"points":2380,"fill":2459,"style":2460},"polygon",[2381,2384,2387,2390,2393,2396,2399,2402,2405,2408,2410,2412,2414,2416,2418,2420,2422,2424,2426,2428,2431,2434,2437,2440,2443,2446,2447,2449,2451,2453,2455,2457],[2382,2383],-1.8,0,[2385,2386],-1.773,-0.094,[2388,2389],-1.691,-0.185,[2391,2392],-1.559,-0.27,[2394,2395],-1.379,-0.347,[2397,2398],-1.157,-0.414,[2400,2401],-0.9,-0.468,[2403,2404],-0.616,-0.507,[2406,2407],-0.313,-0.532,[2383,2409],-0.54,[2411,2407],0.313,[2413,2404],0.616,[2415,2401],0.9,[2417,2398],1.157,[2419,2395],1.379,[2421,2392],1.559,[2423,2389],1.691,[2425,2386],1.773,[2427,2383],1.8,[2429,2430],1,2.2,[2432,2433],0.966,2.278,[2435,2436],0.866,2.35,[2438,2439],0.707,2.412,[2441,2442],0.5,2.46,[2444,2445],0.259,2.49,[2383,2373],[2448,2445],-0.259,[2450,2442],-0.5,[2452,2439],-0.707,[2454,2436],-0.866,[2456,2433],-0.966,[2458,2430],-1,true,"muted",{"type":2462,"center":2463,"rx":2427,"ry":2464,"start":2383,"end":2465,"style":2466},"ellipse",[2383,2383],0.54,180,"dashed",{"type":2462,"center":2468,"rx":2427,"ry":2464,"start":2465,"end":2469},[2383,2383],360,{"type":2471,"from":2472,"to":2473},"segment",[2382,2383],[2458,2430],{"type":2471,"from":2475,"to":2476},[2427,2383],[2429,2430],{"type":2462,"center":2478,"rx":2429,"ry":2479},[2383,2430],0.3,{"type":2471,"from":2481,"to":2482},[2383,2383],[2427,2383],{"type":2471,"from":2484,"to":2485},[2383,2430],[2429,2430],{"type":2471,"from":2487,"to":2488,"style":2466},[2383,2383],[2383,2430],{"type":2490,"at":2491,"from":2492,"to":2493},"rightAngle",[2383,2383],[2383,2430],[2427,2383],{"type":2495,"at":2496},"point",[2383,2383],{"type":2495,"at":2498},[2383,2430],{"type":2500,"at":2501,"text":609},"label",[2415,2502],-0.25,{"type":2500,"at":2504,"text":702},[2505,2506],1.3,2.45,{"type":2500,"at":2508,"text":927},[2502,2509],1.1,{"type":2500,"at":2511,"text":798},[2512,2513],1.72,1.15,"\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 den Radien R und r, der Höhe h und der Mantellinie s\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-cone-frustum-surface-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-cone-frustum-surface-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>\u003Ctext x=\"192.96\" y=\"86.4\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">s\u003C\u002Ftext>\u003C\u002Fsvg>","cone-frustum-surface","\\begin{gathered} O = \\pi \\left(R^2 + r^2 + (R + r)\\, s\\right) \\\\ s = \\sqrt{(R - r)^2 + h^2} \\end{gathered}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmtable rowspacing=\"0.25em\" columnalign=\"center\" columnspacing=\"0em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmi>O\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>π\u003C\u002Fmi>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmi>R\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>R\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>r\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>s\u003C\u002Fmi>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmi>s\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsqrt>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>R\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>r\u003C\u002Fmi>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>h\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003C\u002Fmtable>\u003Cannotation encoding=\"application\u002Fx-tex\">\\begin{gathered} O = \\pi \\left(R^2 + r^2 + (R + r)\\, s\\right) \\\\ s = \\sqrt{(R - r)^2 + h^2} \\end{gathered}\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:2.868em;vertical-align:-1.184em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.684em;\">\u003Cspan style=\"top:-3.8199em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">O\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>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\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\">\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=\"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=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">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 mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.176em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">s\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>\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9839em;\">\u003Cspan class=\"svg-align\" style=\"top:-3.2em;\">\u003Cspan class=\"pstrut\" style=\"height:3.2em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\" style=\"padding-left:1em;\">\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">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 mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7401em;\">\u003Cspan style=\"top:-2.989em;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\">\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7401em;\">\u003Cspan style=\"top:-2.989em;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>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.9439em;\">\u003Cspan class=\"pstrut\" style=\"height:3.2em;\">\u003C\u002Fspan>\u003Cspan class=\"hide-tail\" style=\"min-width:1.02em;height:1.28em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"400em\" height=\"1.28em\" viewBox=\"0 0 400000 1296\" preserveAspectRatio=\"xMinYMin slice\">\u003Cpath d=\"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2561em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:1.184em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kegelstumpf",[],[2523,2524,2525],"frustum-volume","cone-surface","pythagorean-theorem",{"title":548,"description":2343},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kegelstumpf","Die Oberfläche eines Kegelstumpfs besteht aus zwei Kreisen und dem Mantel π(R + r)s.",[2530,2531,2532,2533,2534],"kegelstumpf","oberfläche","mantelfläche","kegel","mantellinie",[2536,2539,2542,2545,2548],{"symbol":1825,"meaning":2537,"symbolHtml":2538},"Oberfläche (Grundkreis, Deckkreis und Mantel)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>O\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">O\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:0.0278em;\">O\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":609,"meaning":2540,"symbolHtml":2541},"Radius des Grundkreises","\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":702,"meaning":2543,"symbolHtml":2544},"Radius des Deckkreises","\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":798,"meaning":2546,"symbolHtml":2547},"Mantellinie, die schräge Seitenlänge","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>s\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">s\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\">s\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":927,"meaning":2549,"symbolHtml":2550},"Höhe des Stumpfs","\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>","HaOlVZFh3vTVLWfRjPOvpyOGisvRD9El7e1gGRu4Gog",[2553,2556,2559],{"stem":2554,"title":2555,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kegel","Oberfläche eines Kegels",{"stem":2557,"title":2558,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-pythagoras","Satz des Pythagoras",{"stem":2560,"title":2561,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-kegelstumpf","Volumen eines Kegelstumpfs",1793824269482]