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= 4 \\cdot \\pi \\cdot (5\\,\\text{cm})^2 = 100\\pi\\,\\text{cm}^2 \\approx 314{,}16\\,\\text{cm}^2",[572,991,993,1011,1031,1050,1114,1170],{"className":992,"ariaHidden":602},[601],[572,994,996,999,1002,1005,1008],{"className":995},[606],[572,997],{"className":998,"style":777},[610],[572,1000,752],{"className":1001,"style":617},[615,616],[572,1003],{"className":1004,"style":785},[784],[572,1006,756],{"className":1007},[789],[572,1009],{"className":1010,"style":785},[784],[572,1012,1014,1017,1020,1024,1028],{"className":1013},[606],[572,1015],{"className":1016,"style":894},[610],[572,1018,933],{"className":1019},[615],[572,1021],{"className":1022,"style":1023},[784],"margin-right:0.2222em;",[572,1025,936],{"className":1026},[1027],"mbin",[572,1029],{"className":1030,"style":1023},[784],[572,1032,1034,1038,1041,1044,1047],{"className":1033},[606],[572,1035],{"className":1036,"style":1037},[610],"height:0.4445em;",[572,1039,636],{"className":1040,"style":662},[615,616],[572,1042],{"className":1043,"style":1023},[784],[572,1045,936],{"className":1046},[1027],[572,1048],{"className":1049,"style":1023},[784],[572,1051,1053,1057,1061,1064,1067,1073,1105,1108,1111],{"className":1052},[606],[572,1054],{"className":1055,"style":1056},[610],"height:1.1141em;vertical-align:-0.25em;",[572,1058,944],{"className":1059},[1060],"mopen",[572,1062,856],{"className":1063},[615],[572,1065],{"className":1066,"style":901},[784],[572,1068,1070],{"className":1069},[615,905],[572,1071,863],{"className":1072},[615],[572,1074,1077,1080],{"className":1075},[1076],"mclose",[572,1078,955],{"className":1079},[1076],[572,1081,1083],{"className":1082},[672],[572,1084,1086],{"className":1085},[676],[572,1087,1089],{"className":1088},[680],[572,1090,1093],{"className":1091,"style":1092},[684],"height:0.8641em;",[572,1094,1096,1099],{"style":1095},"top:-3.113em;margin-right:0.05em;",[572,1097],{"className":1098,"style":692},[691],[572,1100,1102],{"className":1101},[696,697,698,699],[572,1103,645],{"className":1104},[615,699],[572,1106],{"className":1107,"style":785},[784],[572,1109,756],{"className":1110},[789],[572,1112],{"className":1113,"style":785},[784],[572,1115,1117,1120,1123,1126,1129,1161,1164,1167],{"className":1116},[606],[572,1118],{"className":1119,"style":1092},[610],[572,1121,962],{"className":1122},[615],[572,1124,636],{"className":1125,"style":662},[615,616],[572,1127],{"className":1128,"style":901},[784],[572,1130,1132,1138],{"className":1131},[615],[572,1133,1135],{"className":1134},[615,905],[572,1136,863],{"className":1137},[615],[572,1139,1141],{"className":1140},[672],[572,1142,1144],{"className":1143},[676],[572,1145,1147],{"className":1146},[680],[572,1148,1150],{"className":1149,"style":1092},[684],[572,1151,1152,1155],{"style":1095},[572,1153],{"className":1154,"style":692},[691],[572,1156,1158],{"className":1157},[696,697,698,699],[572,1159,645],{"className":1160},[615,699],[572,1162],{"className":1163,"style":785},[784],[572,1165,975],{"className":1166},[789],[572,1168],{"className":1169,"style":785},[784],[572,1171,1173,1177,1181,1189,1193,1196],{"className":1172},[606],[572,1174],{"className":1175,"style":1176},[610],"height:1.0585em;vertical-align:-0.1944em;",[572,1178,1180],{"className":1179},[615],"314",[572,1182,1184],{"className":1183},[615],[572,1185,1188],{"className":1186},[1187],"mpunct",",",[572,1190,1192],{"className":1191},[615],"16",[572,1194],{"className":1195,"style":901},[784],[572,1197,1199,1205],{"className":1198},[615],[572,1200,1202],{"className":1201},[615,905],[572,1203,863],{"className":1204},[615],[572,1206,1208],{"className":1207},[672],[572,1209,1211],{"className":1210},[676],[572,1212,1214],{"className":1213},[680],[572,1215,1217],{"className":1216,"style":1092},[684],[572,1218,1219,1222],{"style":1095},[572,1220],{"className":1221,"style":692},[691],[572,1223,1225],{"className":1224},[696,697,698,699],[572,1226,645],{"className":1227},[615,699],[563,1229,1230,1231,1275],{},"Die Erde hat ungefähr den Radius ",[572,1232,1234,1254],{"className":1233},[575],[572,1235,1237],{"className":1236},[579],[581,1238,1239],{"xmlns":583},[585,1240,1241,1251],{},[588,1242,1243,1246,1248],{},[643,1244,1245],{},"6371",[858,1247,860],{},[858,1249,1250],{},"km",[595,1252,1253],{"encoding":597},"6371\\,\\text{km}",[572,1255,1257],{"className":1256,"ariaHidden":602},[601],[572,1258,1260,1263,1266,1269],{"className":1259},[606],[572,1261],{"className":1262,"style":733},[610],[572,1264,1245],{"className":1265},[615],[572,1267],{"className":1268,"style":901},[784],[572,1270,1272],{"className":1271},[615,905],[572,1273,1250],{"className":1274},[615],". Wenn man sie als Kugel betrachtet:",[572,1277,1279],{"className":1278},[913],[572,1280,1282,1338],{"className":1281},[575],[572,1283,1285],{"className":1284},[579],[581,1286,1287],{"xmlns":583,"display":922},[585,1288,1289,1335],{},[588,1290,1291,1293,1295,1297,1299,1301,1303,1305,1307,1309,1311,1317,1319,1322,1324,1327,1329],{},[591,1292,752],{},[754,1294,756],{},[643,1296,933],{},[754,1298,936],{},[591,1300,636],{},[754,1302,936],{},[754,1304,944],{"stretchy":943},[643,1306,1245],{},[858,1308,860],{},[858,1310,1250],{},[638,1312,1313,1315],{},[754,1314,955],{"stretchy":943},[643,1316,645],{},[754,1318,975],{},[643,1320,1321],{},"510",[858,1323,860],{},[858,1325,1326],{},"Mio.",[858,1328,860],{},[638,1330,1331,1333],{},[858,1332,1250],{},[643,1334,645],{},[595,1336,1337],{"encoding":597},"O = 4 \\cdot \\pi \\cdot (6371\\,\\text{km})^2 \\approx 510\\,\\text{Mio.}\\,\\text{km}^2",[572,1339,1341,1359,1377,1395,1454],{"className":1340,"ariaHidden":602},[601],[572,1342,1344,1347,1350,1353,1356],{"className":1343},[606],[572,1345],{"className":1346,"style":777},[610],[572,1348,752],{"className":1349,"style":617},[615,616],[572,1351],{"className":1352,"style":785},[784],[572,1354,756],{"className":1355},[789],[572,1357],{"className":1358,"style":785},[784],[572,1360,1362,1365,1368,1371,1374],{"className":1361},[606],[572,1363],{"className":1364,"style":894},[610],[572,1366,933],{"className":1367},[615],[572,1369],{"className":1370,"style":1023},[784],[572,1372,936],{"className":1373},[1027],[572,1375],{"className":1376,"style":1023},[784],[572,1378,1380,1383,1386,1389,1392],{"className":1379},[606],[572,1381],{"className":1382,"style":1037},[610],[572,1384,636],{"className":1385,"style":662},[615,616],[572,1387],{"className":1388,"style":1023},[784],[572,1390,936],{"className":1391},[1027],[572,1393],{"className":1394,"style":1023},[784],[572,1396,1398,1401,1404,1407,1410,1416,1445,1448,1451],{"className":1397},[606],[572,1399],{"className":1400,"style":1056},[610],[572,1402,944],{"className":1403},[1060],[572,1405,1245],{"className":1406},[615],[572,1408],{"className":1409,"style":901},[784],[572,1411,1413],{"className":1412},[615,905],[572,1414,1250],{"className":1415},[615],[572,1417,1419,1422],{"className":1418},[1076],[572,1420,955],{"className":1421},[1076],[572,1423,1425],{"className":1424},[672],[572,1426,1428],{"className":1427},[676],[572,1429,1431],{"className":1430},[680],[572,1432,1434],{"className":1433,"style":1092},[684],[572,1435,1436,1439],{"style":1095},[572,1437],{"className":1438,"style":692},[691],[572,1440,1442],{"className":1441},[696,697,698,699],[572,1443,645],{"className":1444},[615,699],[572,1446],{"className":1447,"style":785},[784],[572,1449,975],{"className":1450},[789],[572,1452],{"className":1453,"style":785},[784],[572,1455,1457,1461,1464,1467,1473,1476],{"className":1456},[606],[572,1458],{"className":1459,"style":1460},[610],"height:0.8984em;",[572,1462,1321],{"className":1463},[615],[572,1465],{"className":1466,"style":901},[784],[572,1468,1470],{"className":1469},[615,905],[572,1471,1326],{"className":1472},[615],[572,1474],{"className":1475,"style":901},[784],[572,1477,1479,1485],{"className":1478},[615],[572,1480,1482],{"className":1481},[615,905],[572,1483,1250],{"className":1484},[615],[572,1486,1488],{"className":1487},[672],[572,1489,1491],{"className":1490},[676],[572,1492,1494],{"className":1493},[680],[572,1495,1497],{"className":1496,"style":1460},[684],[572,1498,1500,1503],{"style":1499},"top:-3.1473em;margin-right:0.05em;",[572,1501],{"className":1502,"style":692},[691],[572,1504,1506],{"className":1505},[696,697,698,699],[572,1507,645],{"className":1508},[615,699],[558,1510,1512],{"id":1511},"typische-fehler","Typische Fehler",[1514,1515,1516,1613,1736],"ul",{},[1517,1518,1519,1520,1548,1549,1612],"li",{},"Das ",[572,1521,1523,1536],{"className":1522},[575],[572,1524,1526],{"className":1525},[579],[581,1527,1528],{"xmlns":583},[585,1529,1530,1534],{},[588,1531,1532],{},[643,1533,933],{},[595,1535,933],{"encoding":597},[572,1537,1539],{"className":1538,"ariaHidden":602},[601],[572,1540,1542,1545],{"className":1541},[606],[572,1543],{"className":1544,"style":894},[610],[572,1546,933],{"className":1547},[615]," vergessen. ",[572,1550,1552,1571],{"className":1551},[575],[572,1553,1555],{"className":1554},[579],[581,1556,1557],{"xmlns":583},[585,1558,1559,1569],{},[588,1560,1561,1563],{},[591,1562,636],{},[638,1564,1565,1567],{},[591,1566,593],{},[643,1568,645],{},[595,1570,648],{"encoding":597},[572,1572,1574],{"className":1573,"ariaHidden":602},[601],[572,1575,1577,1580,1583],{"className":1576},[606],[572,1578],{"className":1579,"style":658},[610],[572,1581,636],{"className":1582,"style":662},[615,616],[572,1584,1586,1589],{"className":1585},[615],[572,1587,593],{"className":1588,"style":617},[615,616],[572,1590,1592],{"className":1591},[672],[572,1593,1595],{"className":1594},[676],[572,1596,1598],{"className":1597},[680],[572,1599,1601],{"className":1600,"style":658},[684],[572,1602,1603,1606],{"style":687},[572,1604],{"className":1605,"style":692},[691],[572,1607,1609],{"className":1608},[696,697,698,699],[572,1610,645],{"className":1611},[615,699]," ist nur die Fläche des Querschnittskreises.",[1517,1614,1615,1675,1676,1735],{},[572,1616,1618,1637],{"className":1617},[575],[572,1619,1621],{"className":1620},[579],[581,1622,1623],{"xmlns":583},[585,1624,1625,1634],{},[588,1626,1627],{},[638,1628,1629,1631],{},[591,1630,593],{},[643,1632,1633],{},"3",[595,1635,1636],{"encoding":597},"r^3",[572,1638,1640],{"className":1639,"ariaHidden":602},[601],[572,1641,1643,1646],{"className":1642},[606],[572,1644],{"className":1645,"style":658},[610],[572,1647,1649,1652],{"className":1648},[615],[572,1650,593],{"className":1651,"style":617},[615,616],[572,1653,1655],{"className":1654},[672],[572,1656,1658],{"className":1657},[676],[572,1659,1661],{"className":1660},[680],[572,1662,1664],{"className":1663,"style":658},[684],[572,1665,1666,1669],{"style":687},[572,1667],{"className":1668,"style":692},[691],[572,1670,1672],{"className":1671},[696,697,698,699],[572,1673,1633],{"className":1674},[615,699]," statt ",[572,1677,1679,1697],{"className":1678},[575],[572,1680,1682],{"className":1681},[579],[581,1683,1684],{"xmlns":583},[585,1685,1686,1694],{},[588,1687,1688],{},[638,1689,1690,1692],{},[591,1691,593],{},[643,1693,645],{},[595,1695,1696],{"encoding":597},"r^2",[572,1698,1700],{"className":1699,"ariaHidden":602},[601],[572,1701,1703,1706],{"className":1702},[606],[572,1704],{"className":1705,"style":658},[610],[572,1707,1709,1712],{"className":1708},[615],[572,1710,593],{"className":1711,"style":617},[615,616],[572,1713,1715],{"className":1714},[672],[572,1716,1718],{"className":1717},[676],[572,1719,1721],{"className":1720},[680],[572,1722,1724],{"className":1723,"style":658},[684],[572,1725,1726,1729],{"style":687},[572,1727],{"className":1728,"style":692},[691],[572,1730,1732],{"className":1731},[696,697,698,699],[572,1733,645],{"className":1734},[615,699]," nehmen. Eine Fläche hat immer nur zwei Längen-Dimensionen.",[1517,1737,1738,1739,1808],{},"Den Durchmesser in ",[572,1740,1742,1764],{"className":1741},[575],[572,1743,1745],{"className":1744},[579],[581,1746,1747],{"xmlns":583},[585,1748,1749,1761],{},[588,1750,1751,1753,1755],{},[643,1752,933],{},[591,1754,636],{},[638,1756,1757,1759],{},[591,1758,593],{},[643,1760,645],{},[595,1762,1763],{"encoding":597},"4\\pi r^2",[572,1765,1767],{"className":1766,"ariaHidden":602},[601],[572,1768,1770,1773,1776,1779],{"className":1769},[606],[572,1771],{"className":1772,"style":658},[610],[572,1774,933],{"className":1775},[615],[572,1777,636],{"className":1778,"style":662},[615,616],[572,1780,1782,1785],{"className":1781},[615],[572,1783,593],{"className":1784,"style":617},[615,616],[572,1786,1788],{"className":1787},[672],[572,1789,1791],{"className":1790},[676],[572,1792,1794],{"className":1793},[680],[572,1795,1797],{"className":1796,"style":658},[684],[572,1798,1799,1802],{"style":687},[572,1800],{"className":1801,"style":692},[691],[572,1803,1805],{"className":1804},[696,697,698,699],[572,1806,645],{"className":1807},[615,699]," einsetzen. Das ergibt das Vierfache.",{"title":1810,"searchDepth":1811,"depth":1811,"links":1812},"",2,[1813,1814,1815],{"id":560,"depth":1811,"text":561},{"id":833,"depth":1811,"text":834},{"id":1511,"depth":1811,"text":1512},[1817,1820,1823,1826],{"lhs":1818,"rhs":1819},"4 * pi * r^2","pi * (2*r)^2",{"lhs":1821,"rhs":1822},"4 * pi * 5^2","100 * pi",{"lhs":1824,"rhs":1825},"round(100 * pi, 2)","314.16",{"lhs":1827,"rhs":1321},"round(4 * pi * 6371^2 \u002F 10^6)",null,"md",{"caption":1831,"x":1832,"y":1835,"items":1836},"Kugel mit dem Mittelpunkt M und dem Radius r; die Oberfläche O ist die gewölbte Hülle",[1833,1834],-2.45,2.45,[1833,1834],[1837,1842,1847,1851,1855,1862,1867],{"type":1838,"center":1839,"rx":1811,"ry":1811,"fill":1841},"ellipse",[1840,1840],0,true,{"type":1838,"center":1843,"rx":1811,"ry":1844,"start":1840,"end":1845,"style":1846},[1840,1840],0.6,180,"dashed",{"type":1838,"center":1848,"rx":1811,"ry":1844,"start":1845,"end":1849,"style":1850},[1840,1840],360,"muted",{"type":1852,"from":1853,"to":1854},"segment",[1840,1840],[1811,1840],{"type":1856,"at":1857,"label":1858,"offset":1859},"point",[1840,1840],"M",[1860,1861],-6,16,{"type":1863,"at":1864,"text":593},"label",[1865,1866],1,0.22,{"type":1863,"at":1868,"text":752},[1869,1869],1.62,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 235.2 235.2\" width=\"235.2\" height=\"235.2\" role=\"img\" aria-label=\"Kugel mit dem Mittelpunkt M und dem Radius r; die Oberfläche O ist die gewölbte Hülle\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-sphere-surface-arrow\" 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