[{"data":1,"prerenderedAt":3130},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kegel":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kegel":3117},[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":2955,"conditions":2976,"conditionsHtml":2976,"deprecated":2976,"description":2948,"extension":2977,"figure":2978,"figureCaption":2979,"figureHtml":3080,"formulaId":3081,"latex":3082,"latexHtml":3083,"level":3084,"meta":3085,"navigation":3046,"path":3086,"redirectFrom":3087,"related":3088,"seo":3093,"stem":3094,"subject":589,"summary":3095,"tags":3096,"variables":3102,"__hash__":3116},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kegel.md","Oberfläche eines Kegels",[550,551,552,553,554],"Oberfläche Kegel","Oberfläche Kegel berechnen","Mantelfläche Kegel","Kegel Mantellinie","O = πr² + πrs",{"type":556,"value":557,"toc":2947},"minimark",[558,563,572,756,823,1031,1035,1108,1299,1303,1443,1670,1673,2197,2332,2604,2608],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,571],"p",{},"Die Formel gilt für den ",[568,569,570],"strong",{},"geraden Kreiskegel",", bei dem die Spitze genau über dem Mittelpunkt des Grundkreises liegt. Die Oberfläche besteht aus zwei Teilen:",[573,574,575,678],"ul",{},[576,577,578,579],"li",{},"der Grundfläche, einem Kreis: ",[580,581,584,617],"span",{"className":582},[583],"katex",[580,585,588],{"className":586},[587],"katex-mathml",[589,590,592],"math",{"xmlns":591},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[593,594,595,612],"semantics",{},[596,597,598,602],"mrow",{},[599,600,601],"mi",{},"π",[603,604,605,608],"msup",{},[599,606,607],{},"r",[609,610,611],"mn",{},"2",[613,614,616],"annotation",{"encoding":615},"application\u002Fx-tex","\\pi r^2",[580,618,622],{"className":619,"ariaHidden":621},[620],"katex-html","true",[580,623,626,631,637],{"className":624},[625],"base",[580,627],{"className":628,"style":630},[629],"strut","height:0.8141em;",[580,632,601],{"className":633,"style":636},[634,635],"mord","mathnormal","margin-right:0.0359em;",[580,638,640,644],{"className":639},[634],[580,641,607],{"className":642,"style":643},[634,635],"margin-right:0.0278em;",[580,645,648],{"className":646},[647],"msupsub",[580,649,652],{"className":650},[651],"vlist-t",[580,653,656],{"className":654},[655],"vlist-r",[580,657,660],{"className":658,"style":630},[659],"vlist",[580,661,663,668],{"style":662},"top:-3.063em;margin-right:0.05em;",[580,664],{"className":665,"style":667},[666],"pstrut","height:2.7em;",[580,669,675],{"className":670},[671,672,673,674],"sizing","reset-size6","size3","mtight",[580,676,611],{"className":677},[634,674],[576,679,680,681,684,685],{},"der ",[568,682,683],{},"Mantelfläche"," ",[580,686,688,714],{"className":687},[583],[580,689,691],{"className":690},[587],[589,692,693],{"xmlns":591},[593,694,695,711],{},[596,696,697,700,704,706,708],{},[599,698,699],{},"M",[701,702,703],"mo",{},"=",[599,705,601],{},[599,707,607],{},[599,709,710],{},"s",[613,712,713],{"encoding":615},"M = \\pi r s",[580,715,717,740],{"className":716,"ariaHidden":621},[620],[580,718,720,724,728,733,737],{"className":719},[625],[580,721],{"className":722,"style":723},[629],"height:0.6833em;",[580,725,699],{"className":726,"style":727},[634,635],"margin-right:0.109em;",[580,729],{"className":730,"style":732},[731],"mspace","margin-right:0.2778em;",[580,734,703],{"className":735},[736],"mrel",[580,738],{"className":739,"style":732},[731],[580,741,743,747,750,753],{"className":742},[625],[580,744],{"className":745,"style":746},[629],"height:0.4306em;",[580,748,601],{"className":749,"style":636},[634,635],[580,751,607],{"className":752,"style":643},[634,635],[580,754,710],{"className":755},[634,635],[564,757,758,759,787,788,791,792,822],{},"Dabei ist ",[580,760,762,775],{"className":761},[583],[580,763,765],{"className":764},[587],[589,766,767],{"xmlns":591},[593,768,769,773],{},[596,770,771],{},[599,772,710],{},[613,774,710],{"encoding":615},[580,776,778],{"className":777,"ariaHidden":621},[620],[580,779,781,784],{"className":780},[625],[580,782],{"className":783,"style":746},[629],[580,785,710],{"className":786},[634,635]," die ",[568,789,790],{},"Mantellinie",": die schräge Strecke von der Spitze bis zum Rand des Grundkreises. Sie ist nicht die Höhe ",[580,793,795,809],{"className":794},[583],[580,796,798],{"className":797},[587],[589,799,800],{"xmlns":591},[593,801,802,807],{},[596,803,804],{},[599,805,806],{},"h",[613,808,806],{"encoding":615},[580,810,812],{"className":811,"ariaHidden":621},[620],[580,813,815,819],{"className":814},[625],[580,816],{"className":817,"style":818},[629],"height:0.6944em;",[580,820,806],{"className":821},[634,635],". Höhe, Radius und Mantellinie bilden ein rechtwinkliges Dreieck, deshalb gilt nach Pythagoras:",[580,824,827],{"className":825},[826],"katex-display",[580,828,830,867],{"className":829},[583],[580,831,833],{"className":832},[587],[589,834,836],{"xmlns":591,"display":835},"block",[593,837,838,864],{},[596,839,840,842,844],{},[599,841,710],{},[701,843,703],{},[845,846,847],"msqrt",{},[596,848,849,855,858],{},[603,850,851,853],{},[599,852,607],{},[609,854,611],{},[701,856,857],{},"+",[603,859,860,862],{},[599,861,806],{},[609,863,611],{},[613,865,866],{"encoding":615},"s = \\sqrt{r^2 + h^2}",[580,868,870,888],{"className":869,"ariaHidden":621},[620],[580,871,873,876,879,882,885],{"className":872},[625],[580,874],{"className":875,"style":746},[629],[580,877,710],{"className":878},[634,635],[580,880],{"className":881,"style":732},[731],[580,883,703],{"className":884},[736],[580,886],{"className":887,"style":732},[731],[580,889,891,895],{"className":890},[625],[580,892],{"className":893,"style":894},[629],"height:1.24em;vertical-align:-0.1777em;",[580,896,899],{"className":897},[634,898],"sqrt",[580,900,903,1022],{"className":901},[651,902],"vlist-t2",[580,904,906,1017],{"className":905},[655],[580,907,910,994],{"className":908,"style":909},[659],"height:1.0623em;",[580,911,915,919],{"className":912,"style":914},[913],"svg-align","top:-3.2em;",[580,916],{"className":917,"style":918},[666],"height:3.2em;",[580,920,923,954,958,962,965],{"className":921,"style":922},[634],"padding-left:1em;",[580,924,926,929],{"className":925},[634],[580,927,607],{"className":928,"style":643},[634,635],[580,930,932],{"className":931},[647],[580,933,935],{"className":934},[651],[580,936,938],{"className":937},[655],[580,939,942],{"className":940,"style":941},[659],"height:0.7401em;",[580,943,945,948],{"style":944},"top:-2.989em;margin-right:0.05em;",[580,946],{"className":947,"style":667},[666],[580,949,951],{"className":950},[671,672,673,674],[580,952,611],{"className":953},[634,674],[580,955],{"className":956,"style":957},[731],"margin-right:0.2222em;",[580,959,857],{"className":960},[961],"mbin",[580,963],{"className":964,"style":957},[731],[580,966,968,971],{"className":967},[634],[580,969,806],{"className":970},[634,635],[580,972,974],{"className":973},[647],[580,975,977],{"className":976},[651],[580,978,980],{"className":979},[655],[580,981,983],{"className":982,"style":941},[659],[580,984,985,988],{"style":944},[580,986],{"className":987,"style":667},[666],[580,989,991],{"className":990},[671,672,673,674],[580,992,611],{"className":993},[634,674],[580,995,997,1000],{"style":996},"top:-3.0223em;",[580,998],{"className":999,"style":918},[666],[580,1001,1005],{"className":1002,"style":1004},[1003],"hide-tail","min-width:1.02em;height:1.28em;",[1006,1007,1013],"svg",{"xmlns":1008,"width":1009,"height":1010,"viewBox":1011,"preserveAspectRatio":1012},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.28em","0 0 400000 1296","xMinYMin slice",[1014,1015],"path",{"d":1016},"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",[580,1018,1021],{"className":1019},[1020],"vlist-s","​",[580,1023,1025],{"className":1024},[655],[580,1026,1029],{"className":1027,"style":1028},[659],"height:0.1777em;",[580,1030],{},[559,1032,1034],{"id":1033},"herleitung","Herleitung",[564,1036,1037,1038,1066,1067,1107],{},"Schneidet man den Mantel entlang einer Mantellinie auf und legt ihn flach hin, entsteht ein Kreissektor mit dem Radius ",[580,1039,1041,1054],{"className":1040},[583],[580,1042,1044],{"className":1043},[587],[589,1045,1046],{"xmlns":591},[593,1047,1048,1052],{},[596,1049,1050],{},[599,1051,710],{},[613,1053,710],{"encoding":615},[580,1055,1057],{"className":1056,"ariaHidden":621},[620],[580,1058,1060,1063],{"className":1059},[625],[580,1061],{"className":1062,"style":746},[629],[580,1064,710],{"className":1065},[634,635],". Sein Bogen ist so lang wie der Umfang des Grundkreises, also ",[580,1068,1070,1088],{"className":1069},[583],[580,1071,1073],{"className":1072},[587],[589,1074,1075],{"xmlns":591},[593,1076,1077,1085],{},[596,1078,1079,1081,1083],{},[609,1080,611],{},[599,1082,601],{},[599,1084,607],{},[613,1086,1087],{"encoding":615},"2\\pi r",[580,1089,1091],{"className":1090,"ariaHidden":621},[620],[580,1092,1094,1098,1101,1104],{"className":1093},[625],[580,1095],{"className":1096,"style":1097},[629],"height:0.6444em;",[580,1099,611],{"className":1100},[634],[580,1102,601],{"className":1103,"style":636},[634,635],[580,1105,607],{"className":1106,"style":643},[634,635],". Die Fläche eines Kreissektors ist Bogenlänge mal Radius durch 2:",[580,1109,1111],{"className":1110},[826],[580,1112,1114,1156],{"className":1113},[583],[580,1115,1117],{"className":1116},[587],[589,1118,1119],{"xmlns":591,"display":835},[593,1120,1121,1153],{},[596,1122,1123,1125,1127,1145,1147,1149,1151],{},[599,1124,699],{},[701,1126,703],{},[1128,1129,1130,1143],"mfrac",{},[596,1131,1132,1134,1136,1138,1141],{},[609,1133,611],{},[599,1135,601],{},[599,1137,607],{},[701,1139,1140],{},"⋅",[599,1142,710],{},[609,1144,611],{},[701,1146,703],{},[599,1148,601],{},[599,1150,607],{},[599,1152,710],{},[613,1154,1155],{"encoding":615},"M = \\frac{2\\pi r \\cdot s}{2} = \\pi r s",[580,1157,1159,1177,1284],{"className":1158,"ariaHidden":621},[620],[580,1160,1162,1165,1168,1171,1174],{"className":1161},[625],[580,1163],{"className":1164,"style":723},[629],[580,1166,699],{"className":1167,"style":727},[634,635],[580,1169],{"className":1170,"style":732},[731],[580,1172,703],{"className":1173},[736],[580,1175],{"className":1176,"style":732},[731],[580,1178,1180,1184,1275,1278,1281],{"className":1179},[625],[580,1181],{"className":1182,"style":1183},[629],"height:2.0074em;vertical-align:-0.686em;",[580,1185,1187,1192,1271],{"className":1186},[634],[580,1188],{"className":1189},[1190,1191],"mopen","nulldelimiter",[580,1193,1195],{"className":1194},[1128],[580,1196,1198,1262],{"className":1197},[651,902],[580,1199,1201,1259],{"className":1200},[655],[580,1202,1205,1218,1229],{"className":1203,"style":1204},[659],"height:1.3214em;",[580,1206,1208,1212],{"style":1207},"top:-2.314em;",[580,1209],{"className":1210,"style":1211},[666],"height:3em;",[580,1213,1215],{"className":1214},[634],[580,1216,611],{"className":1217},[634],[580,1219,1221,1224],{"style":1220},"top:-3.23em;",[580,1222],{"className":1223,"style":1211},[666],[580,1225],{"className":1226,"style":1228},[1227],"frac-line","border-bottom-width:0.04em;",[580,1230,1232,1235],{"style":1231},"top:-3.677em;",[580,1233],{"className":1234,"style":1211},[666],[580,1236,1238,1241,1244,1247,1250,1253,1256],{"className":1237},[634],[580,1239,611],{"className":1240},[634],[580,1242,601],{"className":1243,"style":636},[634,635],[580,1245,607],{"className":1246,"style":643},[634,635],[580,1248],{"className":1249,"style":957},[731],[580,1251,1140],{"className":1252},[961],[580,1254],{"className":1255,"style":957},[731],[580,1257,710],{"className":1258},[634,635],[580,1260,1021],{"className":1261},[1020],[580,1263,1265],{"className":1264},[655],[580,1266,1269],{"className":1267,"style":1268},[659],"height:0.686em;",[580,1270],{},[580,1272],{"className":1273},[1274,1191],"mclose",[580,1276],{"className":1277,"style":732},[731],[580,1279,703],{"className":1280},[736],[580,1282],{"className":1283,"style":732},[731],[580,1285,1287,1290,1293,1296],{"className":1286},[625],[580,1288],{"className":1289,"style":746},[629],[580,1291,601],{"className":1292,"style":636},[634,635],[580,1294,607],{"className":1295,"style":643},[634,635],[580,1297,710],{"className":1298},[634,635],[559,1300,1302],{"id":1301},"beispiele","Beispiele",[564,1304,1305,1306,1376,1377,1442],{},"Ein Kegel hat den Radius ",[580,1307,1309,1335],{"className":1308},[583],[580,1310,1312],{"className":1311},[587],[589,1313,1314],{"xmlns":591},[593,1315,1316,1332],{},[596,1317,1318,1320,1322,1325,1329],{},[599,1319,607],{},[701,1321,703],{},[609,1323,1324],{},"3",[1326,1327,1328],"mtext",{}," ",[1326,1330,1331],{},"cm",[613,1333,1334],{"encoding":615},"r = 3\\,\\text{cm}",[580,1336,1338,1356],{"className":1337,"ariaHidden":621},[620],[580,1339,1341,1344,1347,1350,1353],{"className":1340},[625],[580,1342],{"className":1343,"style":746},[629],[580,1345,607],{"className":1346,"style":643},[634,635],[580,1348],{"className":1349,"style":732},[731],[580,1351,703],{"className":1352},[736],[580,1354],{"className":1355,"style":732},[731],[580,1357,1359,1362,1365,1369],{"className":1358},[625],[580,1360],{"className":1361,"style":1097},[629],[580,1363,1324],{"className":1364},[634],[580,1366],{"className":1367,"style":1368},[731],"margin-right:0.1667em;",[580,1370,1373],{"className":1371},[634,1372],"text",[580,1374,1331],{"className":1375},[634]," und die Höhe ",[580,1378,1380,1403],{"className":1379},[583],[580,1381,1383],{"className":1382},[587],[589,1384,1385],{"xmlns":591},[593,1386,1387,1400],{},[596,1388,1389,1391,1393,1396,1398],{},[599,1390,806],{},[701,1392,703],{},[609,1394,1395],{},"4",[1326,1397,1328],{},[1326,1399,1331],{},[613,1401,1402],{"encoding":615},"h = 4\\,\\text{cm}",[580,1404,1406,1424],{"className":1405,"ariaHidden":621},[620],[580,1407,1409,1412,1415,1418,1421],{"className":1408},[625],[580,1410],{"className":1411,"style":818},[629],[580,1413,806],{"className":1414},[634,635],[580,1416],{"className":1417,"style":732},[731],[580,1419,703],{"className":1420},[736],[580,1422],{"className":1423,"style":732},[731],[580,1425,1427,1430,1433,1436],{"className":1426},[625],[580,1428],{"className":1429,"style":1097},[629],[580,1431,1395],{"className":1432},[634],[580,1434],{"className":1435,"style":1368},[731],[580,1437,1439],{"className":1438},[634,1372],[580,1440,1331],{"className":1441},[634],". Zuerst die Mantellinie:",[580,1444,1446],{"className":1445},[826],[580,1447,1449,1496],{"className":1448},[583],[580,1450,1452],{"className":1451},[587],[589,1453,1454],{"xmlns":591,"display":835},[593,1455,1456,1493],{},[596,1457,1458,1460,1462,1480,1482,1484,1486,1489,1491],{},[599,1459,710],{},[701,1461,703],{},[845,1463,1464],{},[596,1465,1466,1472,1474],{},[603,1467,1468,1470],{},[609,1469,1324],{},[609,1471,611],{},[701,1473,857],{},[603,1475,1476,1478],{},[609,1477,1395],{},[609,1479,611],{},[1326,1481,1328],{},[1326,1483,1331],{},[701,1485,703],{},[609,1487,1488],{},"5",[1326,1490,1328],{},[1326,1492,1331],{},[613,1494,1495],{"encoding":615},"s = \\sqrt{3^2 + 4^2}\\,\\text{cm} = 5\\,\\text{cm}",[580,1497,1499,1517,1652],{"className":1498,"ariaHidden":621},[620],[580,1500,1502,1505,1508,1511,1514],{"className":1501},[625],[580,1503],{"className":1504,"style":746},[629],[580,1506,710],{"className":1507},[634,635],[580,1509],{"className":1510,"style":732},[731],[580,1512,703],{"className":1513},[736],[580,1515],{"className":1516,"style":732},[731],[580,1518,1520,1523,1634,1637,1643,1646,1649],{"className":1519},[625],[580,1521],{"className":1522,"style":894},[629],[580,1524,1526],{"className":1525},[634,898],[580,1527,1529,1626],{"className":1528},[651,902],[580,1530,1532,1623],{"className":1531},[655],[580,1533,1535,1611],{"className":1534,"style":909},[659],[580,1536,1538,1541],{"className":1537,"style":914},[913],[580,1539],{"className":1540,"style":918},[666],[580,1542,1544,1573,1576,1579,1582],{"className":1543,"style":922},[634],[580,1545,1547,1550],{"className":1546},[634],[580,1548,1324],{"className":1549},[634],[580,1551,1553],{"className":1552},[647],[580,1554,1556],{"className":1555},[651],[580,1557,1559],{"className":1558},[655],[580,1560,1562],{"className":1561,"style":941},[659],[580,1563,1564,1567],{"style":944},[580,1565],{"className":1566,"style":667},[666],[580,1568,1570],{"className":1569},[671,672,673,674],[580,1571,611],{"className":1572},[634,674],[580,1574],{"className":1575,"style":957},[731],[580,1577,857],{"className":1578},[961],[580,1580],{"className":1581,"style":957},[731],[580,1583,1585,1588],{"className":1584},[634],[580,1586,1395],{"className":1587},[634],[580,1589,1591],{"className":1590},[647],[580,1592,1594],{"className":1593},[651],[580,1595,1597],{"className":1596},[655],[580,1598,1600],{"className":1599,"style":941},[659],[580,1601,1602,1605],{"style":944},[580,1603],{"className":1604,"style":667},[666],[580,1606,1608],{"className":1607},[671,672,673,674],[580,1609,611],{"className":1610},[634,674],[580,1612,1613,1616],{"style":996},[580,1614],{"className":1615,"style":918},[666],[580,1617,1619],{"className":1618,"style":1004},[1003],[1006,1620,1621],{"xmlns":1008,"width":1009,"height":1010,"viewBox":1011,"preserveAspectRatio":1012},[1014,1622],{"d":1016},[580,1624,1021],{"className":1625},[1020],[580,1627,1629],{"className":1628},[655],[580,1630,1632],{"className":1631,"style":1028},[659],[580,1633],{},[580,1635],{"className":1636,"style":1368},[731],[580,1638,1640],{"className":1639},[634,1372],[580,1641,1331],{"className":1642},[634],[580,1644],{"className":1645,"style":732},[731],[580,1647,703],{"className":1648},[736],[580,1650],{"className":1651,"style":732},[731],[580,1653,1655,1658,1661,1664],{"className":1654},[625],[580,1656],{"className":1657,"style":1097},[629],[580,1659,1488],{"className":1660},[634],[580,1662],{"className":1663,"style":1368},[731],[580,1665,1667],{"className":1666},[634,1372],[580,1668,1331],{"className":1669},[634],[564,1671,1672],{},"Dann die Oberfläche:",[580,1674,1676],{"className":1675},[826],[580,1677,1679,1796],{"className":1678},[583],[580,1680,1682],{"className":1681},[587],[589,1683,1684],{"xmlns":591,"display":835},[593,1685,1686,1793],{},[596,1687,1688,1691,1693,1695,1697,1701,1703,1705,1707,1714,1716,1718,1720,1722,1724,1726,1728,1730,1732,1734,1736,1739,1741,1743,1749,1751,1754,1756,1758,1764,1766,1769,1771,1773,1779,1782,1785,1787],{},[599,1689,1690],{},"O",[701,1692,703],{},[599,1694,601],{},[701,1696,1140],{},[701,1698,1700],{"stretchy":1699},"false","(",[609,1702,1324],{},[1326,1704,1328],{},[1326,1706,1331],{},[603,1708,1709,1712],{},[701,1710,1711],{"stretchy":1699},")",[609,1713,611],{},[701,1715,857],{},[599,1717,601],{},[701,1719,1140],{},[609,1721,1324],{},[1326,1723,1328],{},[1326,1725,1331],{},[701,1727,1140],{},[609,1729,1488],{},[1326,1731,1328],{},[1326,1733,1331],{},[701,1735,703],{},[609,1737,1738],{},"9",[599,1740,601],{},[1326,1742,1328],{},[603,1744,1745,1747],{},[1326,1746,1331],{},[609,1748,611],{},[701,1750,857],{},[609,1752,1753],{},"15",[599,1755,601],{},[1326,1757,1328],{},[603,1759,1760,1762],{},[1326,1761,1331],{},[609,1763,611],{},[701,1765,703],{},[609,1767,1768],{},"24",[599,1770,601],{},[1326,1772,1328],{},[603,1774,1775,1777],{},[1326,1776,1331],{},[609,1778,611],{},[701,1780,1781],{},"≈",[609,1783,1784],{},"75,40",[1326,1786,1328],{},[603,1788,1789,1791],{},[1326,1790,1331],{},[609,1792,611],{},[613,1794,1795],{"encoding":615},"O = \\pi \\cdot (3\\,\\text{cm})^2 + \\pi \\cdot 3\\,\\text{cm} \\cdot 5\\,\\text{cm} = 9\\pi\\,\\text{cm}^2 + 15\\pi\\,\\text{cm}^2 = 24\\pi\\,\\text{cm}^2 \\approx 75{,}40\\,\\text{cm}^2",[580,1797,1799,1817,1836,1898,1916,1943,1970,2027,2083,2139],{"className":1798,"ariaHidden":621},[620],[580,1800,1802,1805,1808,1811,1814],{"className":1801},[625],[580,1803],{"className":1804,"style":723},[629],[580,1806,1690],{"className":1807,"style":643},[634,635],[580,1809],{"className":1810,"style":732},[731],[580,1812,703],{"className":1813},[736],[580,1815],{"className":1816,"style":732},[731],[580,1818,1820,1824,1827,1830,1833],{"className":1819},[625],[580,1821],{"className":1822,"style":1823},[629],"height:0.4445em;",[580,1825,601],{"className":1826,"style":636},[634,635],[580,1828],{"className":1829,"style":957},[731],[580,1831,1140],{"className":1832},[961],[580,1834],{"className":1835,"style":957},[731],[580,1837,1839,1843,1846,1849,1852,1858,1889,1892,1895],{"className":1838},[625],[580,1840],{"className":1841,"style":1842},[629],"height:1.1141em;vertical-align:-0.25em;",[580,1844,1700],{"className":1845},[1190],[580,1847,1324],{"className":1848},[634],[580,1850],{"className":1851,"style":1368},[731],[580,1853,1855],{"className":1854},[634,1372],[580,1856,1331],{"className":1857},[634],[580,1859,1861,1864],{"className":1860},[1274],[580,1862,1711],{"className":1863},[1274],[580,1865,1867],{"className":1866},[647],[580,1868,1870],{"className":1869},[651],[580,1871,1873],{"className":1872},[655],[580,1874,1877],{"className":1875,"style":1876},[659],"height:0.8641em;",[580,1878,1880,1883],{"style":1879},"top:-3.113em;margin-right:0.05em;",[580,1881],{"className":1882,"style":667},[666],[580,1884,1886],{"className":1885},[671,672,673,674],[580,1887,611],{"className":1888},[634,674],[580,1890],{"className":1891,"style":957},[731],[580,1893,857],{"className":1894},[961],[580,1896],{"className":1897,"style":957},[731],[580,1899,1901,1904,1907,1910,1913],{"className":1900},[625],[580,1902],{"className":1903,"style":1823},[629],[580,1905,601],{"className":1906,"style":636},[634,635],[580,1908],{"className":1909,"style":957},[731],[580,1911,1140],{"className":1912},[961],[580,1914],{"className":1915,"style":957},[731],[580,1917,1919,1922,1925,1928,1934,1937,1940],{"className":1918},[625],[580,1920],{"className":1921,"style":1097},[629],[580,1923,1324],{"className":1924},[634],[580,1926],{"className":1927,"style":1368},[731],[580,1929,1931],{"className":1930},[634,1372],[580,1932,1331],{"className":1933},[634],[580,1935],{"className":1936,"style":957},[731],[580,1938,1140],{"className":1939},[961],[580,1941],{"className":1942,"style":957},[731],[580,1944,1946,1949,1952,1955,1961,1964,1967],{"className":1945},[625],[580,1947],{"className":1948,"style":1097},[629],[580,1950,1488],{"className":1951},[634],[580,1953],{"className":1954,"style":1368},[731],[580,1956,1958],{"className":1957},[634,1372],[580,1959,1331],{"className":1960},[634],[580,1962],{"className":1963,"style":732},[731],[580,1965,703],{"className":1966},[736],[580,1968],{"className":1969,"style":732},[731],[580,1971,1973,1977,1980,1983,1986,2018,2021,2024],{"className":1972},[625],[580,1974],{"className":1975,"style":1976},[629],"height:0.9474em;vertical-align:-0.0833em;",[580,1978,1738],{"className":1979},[634],[580,1981,601],{"className":1982,"style":636},[634,635],[580,1984],{"className":1985,"style":1368},[731],[580,1987,1989,1995],{"className":1988},[634],[580,1990,1992],{"className":1991},[634,1372],[580,1993,1331],{"className":1994},[634],[580,1996,1998],{"className":1997},[647],[580,1999,2001],{"className":2000},[651],[580,2002,2004],{"className":2003},[655],[580,2005,2007],{"className":2006,"style":1876},[659],[580,2008,2009,2012],{"style":1879},[580,2010],{"className":2011,"style":667},[666],[580,2013,2015],{"className":2014},[671,672,673,674],[580,2016,611],{"className":2017},[634,674],[580,2019],{"className":2020,"style":957},[731],[580,2022,857],{"className":2023},[961],[580,2025],{"className":2026,"style":957},[731],[580,2028,2030,2033,2036,2039,2042,2074,2077,2080],{"className":2029},[625],[580,2031],{"className":2032,"style":1876},[629],[580,2034,1753],{"className":2035},[634],[580,2037,601],{"className":2038,"style":636},[634,635],[580,2040],{"className":2041,"style":1368},[731],[580,2043,2045,2051],{"className":2044},[634],[580,2046,2048],{"className":2047},[634,1372],[580,2049,1331],{"className":2050},[634],[580,2052,2054],{"className":2053},[647],[580,2055,2057],{"className":2056},[651],[580,2058,2060],{"className":2059},[655],[580,2061,2063],{"className":2062,"style":1876},[659],[580,2064,2065,2068],{"style":1879},[580,2066],{"className":2067,"style":667},[666],[580,2069,2071],{"className":2070},[671,672,673,674],[580,2072,611],{"className":2073},[634,674],[580,2075],{"className":2076,"style":732},[731],[580,2078,703],{"className":2079},[736],[580,2081],{"className":2082,"style":732},[731],[580,2084,2086,2089,2092,2095,2098,2130,2133,2136],{"className":2085},[625],[580,2087],{"className":2088,"style":1876},[629],[580,2090,1768],{"className":2091},[634],[580,2093,601],{"className":2094,"style":636},[634,635],[580,2096],{"className":2097,"style":1368},[731],[580,2099,2101,2107],{"className":2100},[634],[580,2102,2104],{"className":2103},[634,1372],[580,2105,1331],{"className":2106},[634],[580,2108,2110],{"className":2109},[647],[580,2111,2113],{"className":2112},[651],[580,2114,2116],{"className":2115},[655],[580,2117,2119],{"className":2118,"style":1876},[659],[580,2120,2121,2124],{"style":1879},[580,2122],{"className":2123,"style":667},[666],[580,2125,2127],{"className":2126},[671,672,673,674],[580,2128,611],{"className":2129},[634,674],[580,2131],{"className":2132,"style":732},[731],[580,2134,1781],{"className":2135},[736],[580,2137],{"className":2138,"style":732},[731],[580,2140,2142,2146,2150,2158,2162,2165],{"className":2141},[625],[580,2143],{"className":2144,"style":2145},[629],"height:1.0585em;vertical-align:-0.1944em;",[580,2147,2149],{"className":2148},[634],"75",[580,2151,2153],{"className":2152},[634],[580,2154,2157],{"className":2155},[2156],"mpunct",",",[580,2159,2161],{"className":2160},[634],"40",[580,2163],{"className":2164,"style":1368},[731],[580,2166,2168,2174],{"className":2167},[634],[580,2169,2171],{"className":2170},[634,1372],[580,2172,1331],{"className":2173},[634],[580,2175,2177],{"className":2176},[647],[580,2178,2180],{"className":2179},[651],[580,2181,2183],{"className":2182},[655],[580,2184,2186],{"className":2185,"style":1876},[659],[580,2187,2188,2191],{"style":1879},[580,2189],{"className":2190,"style":667},[666],[580,2192,2194],{"className":2193},[671,672,673,674],[580,2195,611],{"className":2196},[634,674],[564,2198,2199,2200,2265,2266,2331],{},"Ein Partyhut hat keinen Boden, man braucht nur den Mantel. Bei ",[580,2201,2203,2226],{"className":2202},[583],[580,2204,2206],{"className":2205},[587],[589,2207,2208],{"xmlns":591},[593,2209,2210,2223],{},[596,2211,2212,2214,2216,2219,2221],{},[599,2213,607],{},[701,2215,703],{},[609,2217,2218],{},"8",[1326,2220,1328],{},[1326,2222,1331],{},[613,2224,2225],{"encoding":615},"r = 8\\,\\text{cm}",[580,2227,2229,2247],{"className":2228,"ariaHidden":621},[620],[580,2230,2232,2235,2238,2241,2244],{"className":2231},[625],[580,2233],{"className":2234,"style":746},[629],[580,2236,607],{"className":2237,"style":643},[634,635],[580,2239],{"className":2240,"style":732},[731],[580,2242,703],{"className":2243},[736],[580,2245],{"className":2246,"style":732},[731],[580,2248,2250,2253,2256,2259],{"className":2249},[625],[580,2251],{"className":2252,"style":1097},[629],[580,2254,2218],{"className":2255},[634],[580,2257],{"className":2258,"style":1368},[731],[580,2260,2262],{"className":2261},[634,1372],[580,2263,1331],{"className":2264},[634]," und ",[580,2267,2269,2292],{"className":2268},[583],[580,2270,2272],{"className":2271},[587],[589,2273,2274],{"xmlns":591},[593,2275,2276,2289],{},[596,2277,2278,2280,2282,2285,2287],{},[599,2279,710],{},[701,2281,703],{},[609,2283,2284],{},"20",[1326,2286,1328],{},[1326,2288,1331],{},[613,2290,2291],{"encoding":615},"s = 20\\,\\text{cm}",[580,2293,2295,2313],{"className":2294,"ariaHidden":621},[620],[580,2296,2298,2301,2304,2307,2310],{"className":2297},[625],[580,2299],{"className":2300,"style":746},[629],[580,2302,710],{"className":2303},[634,635],[580,2305],{"className":2306,"style":732},[731],[580,2308,703],{"className":2309},[736],[580,2311],{"className":2312,"style":732},[731],[580,2314,2316,2319,2322,2325],{"className":2315},[625],[580,2317],{"className":2318,"style":1097},[629],[580,2320,2284],{"className":2321},[634],[580,2323],{"className":2324,"style":1368},[731],[580,2326,2328],{"className":2327},[634,1372],[580,2329,1331],{"className":2330},[634],":",[580,2333,2335],{"className":2334},[826],[580,2336,2338,2400],{"className":2337},[583],[580,2339,2341],{"className":2340},[587],[589,2342,2343],{"xmlns":591,"display":835},[593,2344,2345,2397],{},[596,2346,2347,2349,2351,2353,2355,2357,2359,2361,2363,2365,2367,2369,2371,2374,2376,2378,2384,2386,2389,2391],{},[599,2348,699],{},[701,2350,703],{},[599,2352,601],{},[701,2354,1140],{},[609,2356,2218],{},[1326,2358,1328],{},[1326,2360,1331],{},[701,2362,1140],{},[609,2364,2284],{},[1326,2366,1328],{},[1326,2368,1331],{},[701,2370,703],{},[609,2372,2373],{},"160",[599,2375,601],{},[1326,2377,1328],{},[603,2379,2380,2382],{},[1326,2381,1331],{},[609,2383,611],{},[701,2385,1781],{},[609,2387,2388],{},"502,65",[1326,2390,1328],{},[603,2392,2393,2395],{},[1326,2394,1331],{},[609,2396,611],{},[613,2398,2399],{"encoding":615},"M = \\pi \\cdot 8\\,\\text{cm} \\cdot 20\\,\\text{cm} = 160\\pi\\,\\text{cm}^2 \\approx 502{,}65\\,\\text{cm}^2",[580,2401,2403,2421,2439,2466,2493,2549],{"className":2402,"ariaHidden":621},[620],[580,2404,2406,2409,2412,2415,2418],{"className":2405},[625],[580,2407],{"className":2408,"style":723},[629],[580,2410,699],{"className":2411,"style":727},[634,635],[580,2413],{"className":2414,"style":732},[731],[580,2416,703],{"className":2417},[736],[580,2419],{"className":2420,"style":732},[731],[580,2422,2424,2427,2430,2433,2436],{"className":2423},[625],[580,2425],{"className":2426,"style":1823},[629],[580,2428,601],{"className":2429,"style":636},[634,635],[580,2431],{"className":2432,"style":957},[731],[580,2434,1140],{"className":2435},[961],[580,2437],{"className":2438,"style":957},[731],[580,2440,2442,2445,2448,2451,2457,2460,2463],{"className":2441},[625],[580,2443],{"className":2444,"style":1097},[629],[580,2446,2218],{"className":2447},[634],[580,2449],{"className":2450,"style":1368},[731],[580,2452,2454],{"className":2453},[634,1372],[580,2455,1331],{"className":2456},[634],[580,2458],{"className":2459,"style":957},[731],[580,2461,1140],{"className":2462},[961],[580,2464],{"className":2465,"style":957},[731],[580,2467,2469,2472,2475,2478,2484,2487,2490],{"className":2468},[625],[580,2470],{"className":2471,"style":1097},[629],[580,2473,2284],{"className":2474},[634],[580,2476],{"className":2477,"style":1368},[731],[580,2479,2481],{"className":2480},[634,1372],[580,2482,1331],{"className":2483},[634],[580,2485],{"className":2486,"style":732},[731],[580,2488,703],{"className":2489},[736],[580,2491],{"className":2492,"style":732},[731],[580,2494,2496,2499,2502,2505,2508,2540,2543,2546],{"className":2495},[625],[580,2497],{"className":2498,"style":1876},[629],[580,2500,2373],{"className":2501},[634],[580,2503,601],{"className":2504,"style":636},[634,635],[580,2506],{"className":2507,"style":1368},[731],[580,2509,2511,2517],{"className":2510},[634],[580,2512,2514],{"className":2513},[634,1372],[580,2515,1331],{"className":2516},[634],[580,2518,2520],{"className":2519},[647],[580,2521,2523],{"className":2522},[651],[580,2524,2526],{"className":2525},[655],[580,2527,2529],{"className":2528,"style":1876},[659],[580,2530,2531,2534],{"style":1879},[580,2532],{"className":2533,"style":667},[666],[580,2535,2537],{"className":2536},[671,672,673,674],[580,2538,611],{"className":2539},[634,674],[580,2541],{"className":2542,"style":732},[731],[580,2544,1781],{"className":2545},[736],[580,2547],{"className":2548,"style":732},[731],[580,2550,2552,2555,2559,2565,2569,2572],{"className":2551},[625],[580,2553],{"className":2554,"style":2145},[629],[580,2556,2558],{"className":2557},[634],"502",[580,2560,2562],{"className":2561},[634],[580,2563,2157],{"className":2564},[2156],[580,2566,2568],{"className":2567},[634],"65",[580,2570],{"className":2571,"style":1368},[731],[580,2573,2575,2581],{"className":2574},[634],[580,2576,2578],{"className":2577},[634,1372],[580,2579,1331],{"className":2580},[634],[580,2582,2584],{"className":2583},[647],[580,2585,2587],{"className":2586},[651],[580,2588,2590],{"className":2589},[655],[580,2591,2593],{"className":2592,"style":1876},[659],[580,2594,2595,2598],{"style":1879},[580,2596],{"className":2597,"style":667},[666],[580,2599,2601],{"className":2600},[671,672,673,674],[580,2602,611],{"className":2603},[634,674],[559,2605,2607],{"id":2606},"typische-fehler","Typische Fehler",[573,2609,2610,2856,2859],{},[576,2611,2612,2613,2641,2642,2670,2671,2855],{},"Die Höhe ",[580,2614,2616,2629],{"className":2615},[583],[580,2617,2619],{"className":2618},[587],[589,2620,2621],{"xmlns":591},[593,2622,2623,2627],{},[596,2624,2625],{},[599,2626,806],{},[613,2628,806],{"encoding":615},[580,2630,2632],{"className":2631,"ariaHidden":621},[620],[580,2633,2635,2638],{"className":2634},[625],[580,2636],{"className":2637,"style":818},[629],[580,2639,806],{"className":2640},[634,635]," statt der Mantellinie ",[580,2643,2645,2658],{"className":2644},[583],[580,2646,2648],{"className":2647},[587],[589,2649,2650],{"xmlns":591},[593,2651,2652,2656],{},[596,2653,2654],{},[599,2655,710],{},[613,2657,710],{"encoding":615},[580,2659,2661],{"className":2660,"ariaHidden":621},[620],[580,2662,2664,2667],{"className":2663},[625],[580,2665],{"className":2666,"style":746},[629],[580,2668,710],{"className":2669},[634,635]," einsetzen. Erst ",[580,2672,2674,2707],{"className":2673},[583],[580,2675,2677],{"className":2676},[587],[589,2678,2679],{"xmlns":591},[593,2680,2681,2705],{},[596,2682,2683,2685,2687],{},[599,2684,710],{},[701,2686,703],{},[845,2688,2689],{},[596,2690,2691,2697,2699],{},[603,2692,2693,2695],{},[599,2694,607],{},[609,2696,611],{},[701,2698,857],{},[603,2700,2701,2703],{},[599,2702,806],{},[609,2704,611],{},[613,2706,866],{"encoding":615},[580,2708,2710,2728],{"className":2709,"ariaHidden":621},[620],[580,2711,2713,2716,2719,2722,2725],{"className":2712},[625],[580,2714],{"className":2715,"style":746},[629],[580,2717,710],{"className":2718},[634,635],[580,2720],{"className":2721,"style":732},[731],[580,2723,703],{"className":2724},[736],[580,2726],{"className":2727,"style":732},[731],[580,2729,2731,2735],{"className":2730},[625],[580,2732],{"className":2733,"style":2734},[629],"height:1.04em;vertical-align:-0.1266em;",[580,2736,2738],{"className":2737},[634,898],[580,2739,2741,2846],{"className":2740},[651,902],[580,2742,2744,2843],{"className":2743},[655],[580,2745,2748,2826],{"className":2746,"style":2747},[659],"height:0.9134em;",[580,2749,2752,2755],{"className":2750,"style":2751},[913],"top:-3em;",[580,2753],{"className":2754,"style":1211},[666],[580,2756,2759,2788,2791,2794,2797],{"className":2757,"style":2758},[634],"padding-left:0.833em;",[580,2760,2762,2765],{"className":2761},[634],[580,2763,607],{"className":2764,"style":643},[634,635],[580,2766,2768],{"className":2767},[647],[580,2769,2771],{"className":2770},[651],[580,2772,2774],{"className":2773},[655],[580,2775,2777],{"className":2776,"style":941},[659],[580,2778,2779,2782],{"style":944},[580,2780],{"className":2781,"style":667},[666],[580,2783,2785],{"className":2784},[671,672,673,674],[580,2786,611],{"className":2787},[634,674],[580,2789],{"className":2790,"style":957},[731],[580,2792,857],{"className":2793},[961],[580,2795],{"className":2796,"style":957},[731],[580,2798,2800,2803],{"className":2799},[634],[580,2801,806],{"className":2802},[634,635],[580,2804,2806],{"className":2805},[647],[580,2807,2809],{"className":2808},[651],[580,2810,2812],{"className":2811},[655],[580,2813,2815],{"className":2814,"style":941},[659],[580,2816,2817,2820],{"style":944},[580,2818],{"className":2819,"style":667},[666],[580,2821,2823],{"className":2822},[671,672,673,674],[580,2824,611],{"className":2825},[634,674],[580,2827,2829,2832],{"style":2828},"top:-2.8734em;",[580,2830],{"className":2831,"style":1211},[666],[580,2833,2836],{"className":2834,"style":2835},[1003],"min-width:0.853em;height:1.08em;",[1006,2837,2840],{"xmlns":1008,"width":1009,"height":2838,"viewBox":2839,"preserveAspectRatio":1012},"1.08em","0 0 400000 1080",[1014,2841],{"d":2842},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[580,2844,1021],{"className":2845},[1020],[580,2847,2849],{"className":2848},[655],[580,2850,2853],{"className":2851,"style":2852},[659],"height:0.1266em;",[580,2854],{}," berechnen.",[576,2857,2858],{},"Die Grundfläche vergessen, wenn die ganze Oberfläche gefragt ist.",[576,2860,2861,2862,2906,2907,2946],{},"Den Mantel wie beim Zylinder mit ",[580,2863,2865,2885],{"className":2864},[583],[580,2866,2868],{"className":2867},[587],[589,2869,2870],{"xmlns":591},[593,2871,2872,2882],{},[596,2873,2874,2876,2878,2880],{},[609,2875,611],{},[599,2877,601],{},[599,2879,607],{},[599,2881,806],{},[613,2883,2884],{"encoding":615},"2\\pi r h",[580,2886,2888],{"className":2887,"ariaHidden":621},[620],[580,2889,2891,2894,2897,2900,2903],{"className":2890},[625],[580,2892],{"className":2893,"style":818},[629],[580,2895,611],{"className":2896},[634],[580,2898,601],{"className":2899,"style":636},[634,635],[580,2901,607],{"className":2902,"style":643},[634,635],[580,2904,806],{"className":2905},[634,635]," berechnen. Beim Kegel ist er ",[580,2908,2910,2928],{"className":2909},[583],[580,2911,2913],{"className":2912},[587],[589,2914,2915],{"xmlns":591},[593,2916,2917,2925],{},[596,2918,2919,2921,2923],{},[599,2920,601],{},[599,2922,607],{},[599,2924,710],{},[613,2926,2927],{"encoding":615},"\\pi r s",[580,2929,2931],{"className":2930,"ariaHidden":621},[620],[580,2932,2934,2937,2940,2943],{"className":2933},[625],[580,2935],{"className":2936,"style":746},[629],[580,2938,601],{"className":2939,"style":636},[634,635],[580,2941,607],{"className":2942,"style":643},[634,635],[580,2944,710],{"className":2945},[634,635],".",{"title":2948,"searchDepth":2949,"depth":2949,"links":2950},"",2,[2951,2952,2953,2954],{"id":561,"depth":2949,"text":562},{"id":1033,"depth":2949,"text":1034},{"id":1301,"depth":2949,"text":1302},{"id":2606,"depth":2949,"text":2607},[2956,2959,2962,2964,2967,2970,2973],{"lhs":2957,"rhs":2958},"pi*r^2 + pi*r*s","pi*r*(r + s)",{"lhs":2960,"rhs":2961},"(2*pi*r) * s \u002F 2","pi*r*s",{"lhs":2963,"rhs":1488},"sqrt(3^2 + 4^2)",{"lhs":2965,"rhs":2966},"pi*3^2 + pi*3*5","24 * pi",{"lhs":2968,"rhs":2969},"round(24 * pi, 2)","75.4",{"lhs":2971,"rhs":2972},"pi*8*20","160 * pi",{"lhs":2974,"rhs":2975},"round(160 * pi, 2)","502.65",null,"md",{"caption":2979,"x":2980,"y":2983,"unit":2986,"items":2987},"Gerader Kreiskegel mit dem Radius r der Grundfläche und der Mantellinie s",[2981,2982],-2.15,2.25,[2984,2985],-0.85,3.45,52,[2988,3048,3055,3058,3062,3065,3068,3071,3076],{"type":2989,"points":2990,"fill":3046,"style":3047},"polygon",[2991,2994,2997,3000,3003,3006,3009,3012,3015,3018,3021,3024,3026,3028,3030,3032,3034,3036,3038,3040,3042,3044],[2992,2993],0,3,[2995,2996],-1.675,0.087,[2998,2999],-1.7,-0.002,[3001,3002],-1.673,-0.09,[3004,3005],-1.596,-0.176,[3007,3008],-1.47,-0.256,[3010,3011],-1.3,-0.329,[3013,3014],-1.091,-0.391,[3016,3017],-0.848,-0.442,[3019,3020],-0.58,-0.479,[3022,3023],-0.295,-0.502,[2992,3025],-0.51,[3027,3023],0.295,[3029,3020],0.58,[3031,3017],0.848,[3033,3014],1.091,[3035,3011],1.3,[3037,3008],1.47,[3039,3005],1.596,[3041,3002],1.673,[3043,2999],1.7,[3045,2996],1.675,true,"muted",{"type":3049,"center":3050,"rx":3043,"ry":3051,"start":3052,"end":3053,"style":3054},"ellipse",[2992,2992],0.51,9.788,170.212,"dashed",{"type":3049,"center":3056,"rx":3043,"ry":3051,"start":3053,"end":3057},[2992,2992],369.788,{"type":3059,"from":3060,"to":3061},"segment",[2995,2996],[2992,2993],{"type":3059,"from":3063,"to":3064},[3045,2996],[2992,2993],{"type":3059,"from":3066,"to":3067},[2992,2992],[3043,2992],{"type":3069,"at":3070},"point",[2992,2992],{"type":3072,"at":3073,"text":607},"label",[3074,3075],0.85,-0.24,{"type":3072,"at":3077,"text":710},[3078,3079],1.138,1.643,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 228.8 223.6\" width=\"228.8\" height=\"223.6\" role=\"img\" aria-label=\"Gerader Kreiskegel mit dem Radius r der Grundfläche und der Mantellinie s\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-cone-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-surface-clip\">\u003Crect x=\"0\" y=\"0\" width=\"228.8\" height=\"223.6\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"111.8,23.4 24.7,174.88 23.4,179.5 24.8,184.08 28.81,188.55 35.36,192.71 44.2,196.51 55.07,199.73 67.7,202.38 81.64,204.31 96.46,205.5 111.8,205.92 127.14,205.5 141.96,204.31 155.9,202.38 168.53,199.73 179.4,196.51 188.24,192.71 194.79,188.55 198.8,184.08 200.2,179.5 198.9,174.88\" class=\"fig-muted fig-fill\"\u002F>\u003Cpath d=\"M 198.91 174.89 A 88.4 26.52 0 0 0 24.69 174.89\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 24.69 174.89 A 88.4 26.52 0 1 0 198.91 174.89\" class=\"fig-main\"\u002F>\u003Cline x1=\"24.7\" y1=\"174.88\" x2=\"111.8\" y2=\"23.4\" class=\"fig-main\"\u002F>\u003Cline x1=\"198.9\" y1=\"174.88\" x2=\"111.8\" y2=\"23.4\" class=\"fig-main\"\u002F>\u003Cline x1=\"111.8\" y1=\"179.4\" x2=\"200.2\" y2=\"179.4\" class=\"fig-main\"\u002F>\u003Ccircle cx=\"111.8\" cy=\"179.4\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"156\" y=\"191.88\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003C\u002Ftext>\u003Ctext x=\"170.98\" y=\"93.96\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">s\u003C\u002Ftext>\u003C\u002Fsvg>","cone-surface","O = \\pi r^2 + \\pi r s","\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>O\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>π\u003C\u002Fmi>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>π\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>s\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">O = \\pi r^2 + \\pi r 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:0.6833em;\">\u003C\u002Fspan>\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>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9474em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\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>\u003C\u002Fspan>\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>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kegel",[],[3089,3090,3091,3092],"cone-volume","pythagorean-theorem","circle-area","cylinder-surface",{"title":548,"description":2948},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kegel","Die Oberfläche eines geraden Kreiskegels ist Grundkreis πr² plus Mantelfläche πrs.",[3097,3098,3099,3100,3101],"oberfläche","kegel","mantelfläche","mantellinie","körper",[3103,3106,3109,3112],{"symbol":1690,"meaning":3104,"symbolHtml":3105},"Oberflächeninhalt des Kegels","\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":607,"meaning":3107,"symbolHtml":3108},"Radius der Grundfläche","\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":710,"meaning":3110,"symbolHtml":3111},"Mantellinie, die Strecke von der Spitze zum Rand der Grundfläche","\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":3113,"meaning":3114,"symbolHtml":3115},"\\pi","Kreiszahl, ungefähr 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>","H1YZo9-Pjqeg36zj2Qqsvk4WqM2bFOXHc-dgpBN4Pno",[3118,3121,3124,3127],{"stem":3119,"title":3120,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-kreis","Flächeninhalt eines Kreises",{"stem":3122,"title":3123,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-zylinder","Oberfläche eines Zylinders",{"stem":3125,"title":3126,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-pythagoras","Satz des Pythagoras",{"stem":3128,"title":3129,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-kegel","Volumen eines Kegels",1793824269466]