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3\\,\\text{cm}",[573,1116,1118,1136],{"className":1117,"ariaHidden":603},[602],[573,1119,1121,1124,1127,1130,1133],{"className":1120},[607],[573,1122],{"className":1123,"style":612},[611],[573,1125,594],{"className":1126,"style":618},[616,617],[573,1128],{"className":1129,"style":732},[731],[573,1131,703],{"className":1132},[736],[573,1134],{"className":1135,"style":732},[731],[573,1137,1139,1142,1145,1149],{"className":1138},[607],[573,1140],{"className":1141,"style":1072},[611],[573,1143,869],{"className":1144},[616],[573,1146],{"className":1147,"style":1148},[731],"margin-right:0.1667em;",[573,1150,1153],{"className":1151},[616,1152],"text",[573,1154,1111],{"className":1155},[616],":",[573,1158,1161],{"className":1159},[1160],"katex-display",[573,1162,1164,1264],{"className":1163},[576],[573,1165,1167],{"className":1166},[580],[582,1168,1170],{"xmlns":584,"display":1169},"block",[586,1171,1172,1261],{},[589,1173,1174,1176,1178,1185,1188,1190,1192,1196,1198,1200,1202,1209,1211,1217,1219,1222,1224,1226,1232,1234,1237,1239,1241,1247,1250,1253,1255],{},[592,1175,852],{},[701,1177,703],{},[705,1179,1180,1183],{},[710,1181,1182],{},"4",[710,1184,869],{},[701,1186,1187],{},"⋅",[592,1189,861],{},[701,1191,1187],{},[701,1193,1195],{"stretchy":1194},"false","(",[710,1197,869],{},[1106,1199,1108],{},[1106,1201,1111],{},[863,1203,1204,1207],{},[701,1205,1206],{"stretchy":1194},")",[710,1208,869],{},[701,1210,703],{},[705,1212,1213,1215],{},[710,1214,1182],{},[710,1216,869],{},[701,1218,1187],{},[710,1220,1221],{},"27",[592,1223,861],{},[1106,1225,1108],{},[863,1227,1228,1230],{},[1106,1229,1111],{},[710,1231,869],{},[701,1233,703],{},[710,1235,1236],{},"36",[592,1238,861],{},[1106,1240,1108],{},[863,1242,1243,1245],{},[1106,1244,1111],{},[710,1246,869],{},[701,1248,1249],{},"≈",[710,1251,1252],{},"113,10",[1106,1254,1108],{},[863,1256,1257,1259],{},[1106,1258,1111],{},[710,1260,869],{},[596,1262,1263],{"encoding":598},"V = \\frac{4}{3} \\cdot \\pi \\cdot (3\\,\\text{cm})^3 = \\frac{4}{3} \\cdot 27\\pi\\,\\text{cm}^3 = 36\\pi\\,\\text{cm}^3 \\approx 113{,}10\\,\\text{cm}^3",[573,1265,1267,1285,1368,1387,1450,1527,1583,1639],{"className":1266,"ariaHidden":603},[602],[573,1268,1270,1273,1276,1279,1282],{"className":1269},[607],[573,1271],{"className":1272,"style":885},[611],[573,1274,852],{"className":1275,"style":889},[616,617],[573,1277],{"className":1278,"style":732},[731],[573,1280,703],{"className":1281},[736],[573,1283],{"className":1284,"style":732},[731],[573,1286,1288,1292,1358,1361,1365],{"className":1287},[607],[573,1289],{"className":1290,"style":1291},[611],"height:2.0074em;vertical-align:-0.686em;",[573,1293,1295,1298,1355],{"className":1294},[616],[573,1296],{"className":1297},[753,754],[573,1299,1301],{"className":1300},[705],[573,1302,1304,1346],{"className":1303},[761,762],[573,1305,1307,1343],{"className":1306},[766],[573,1308,1311,1323,1331],{"className":1309,"style":1310},[770],"height:1.3214em;",[573,1312,1314,1317],{"style":1313},"top:-2.314em;",[573,1315],{"className":1316,"style":779},[778],[573,1318,1320],{"className":1319},[616],[573,1321,869],{"className":1322},[616],[573,1324,1325,1328],{"style":795},[573,1326],{"className":1327,"style":779},[778],[573,1329],{"className":1330,"style":803},[802],[573,1332,1334,1337],{"style":1333},"top:-3.677em;",[573,1335],{"className":1336,"style":779},[778],[573,1338,1340],{"className":1339},[616],[573,1341,1182],{"className":1342},[616],[573,1344,823],{"className":1345},[822],[573,1347,1349],{"className":1348},[766],[573,1350,1353],{"className":1351,"style":1352},[770],"height:0.686em;",[573,1354],{},[573,1356],{"className":1357},[836,754],[573,1359],{"className":1360,"style":889},[731],[573,1362,1187],{"className":1363},[1364],"mbin",[573,1366],{"className":1367,"style":889},[731],[573,1369,1371,1375,1378,1381,1384],{"className":1370},[607],[573,1372],{"className":1373,"style":1374},[611],"height:0.4445em;",[573,1376,861],{"className":1377,"style":961},[616,617],[573,1379],{"className":1380,"style":889},[731],[573,1382,1187],{"className":1383},[1364],[573,1385],{"className":1386,"style":889},[731],[573,1388,1390,1394,1397,1400,1403,1409,1441,1444,1447],{"className":1389},[607],[573,1391],{"className":1392,"style":1393},[611],"height:1.1141em;vertical-align:-0.25em;",[573,1395,1195],{"className":1396},[753],[573,1398,869],{"className":1399},[616],[573,1401],{"className":1402,"style":1148},[731],[573,1404,1406],{"className":1405},[616,1152],[573,1407,1111],{"className":1408},[616],[573,1410,1412,1415],{"className":1411},[836],[573,1413,1206],{"className":1414},[836],[573,1416,1418],{"className":1417},[971],[573,1419,1421],{"className":1420},[761],[573,1422,1424],{"className":1423},[766],[573,1425,1428],{"className":1426,"style":1427},[770],"height:0.8641em;",[573,1429,1431,1435],{"style":1430},"top:-3.113em;margin-right:0.05em;",[573,1432],{"className":1433,"style":1434},[778],"height:2.7em;",[573,1436,1438],{"className":1437},[783,784,785,786],[573,1439,869],{"className":1440},[616,786],[573,1442],{"className":1443,"style":732},[731],[573,1445,703],{"className":1446},[736],[573,1448],{"className":1449,"style":732},[731],[573,1451,1453,1456,1518,1521,1524],{"className":1452},[607],[573,1454],{"className":1455,"style":1291},[611],[573,1457,1459,1462,1515],{"className":1458},[616],[573,1460],{"className":1461},[753,754],[573,1463,1465],{"className":1464},[705],[573,1466,1468,1507],{"className":1467},[761,762],[573,1469,1471,1504],{"className":1470},[766],[573,1472,1474,1485,1493],{"className":1473,"style":1310},[770],[573,1475,1476,1479],{"style":1313},[573,1477],{"className":1478,"style":779},[778],[573,1480,1482],{"className":1481},[616],[573,1483,869],{"className":1484},[616],[573,1486,1487,1490],{"style":795},[573,1488],{"className":1489,"style":779},[778],[573,1491],{"className":1492,"style":803},[802],[573,1494,1495,1498],{"style":1333},[573,1496],{"className":1497,"style":779},[778],[573,1499,1501],{"className":1500},[616],[573,1502,1182],{"className":1503},[616],[573,1505,823],{"className":1506},[822],[573,1508,1510],{"className":1509},[766],[573,1511,1513],{"className":1512,"style":1352},[770],[573,1514],{},[573,1516],{"className":1517},[836,754],[573,1519],{"className":1520,"style":889},[731],[573,1522,1187],{"className":1523},[1364],[573,1525],{"className":1526,"style":889},[731],[573,1528,1530,1533,1536,1539,1542,1574,1577,1580],{"className":1529},[607],[573,1531],{"className":1532,"style":1427},[611],[573,1534,1221],{"className":1535},[616],[573,1537,861],{"className":1538,"style":961},[616,617],[573,1540],{"className":1541,"style":1148},[731],[573,1543,1545,1551],{"className":1544},[616],[573,1546,1548],{"className":1547},[616,1152],[573,1549,1111],{"className":1550},[616],[573,1552,1554],{"className":1553},[971],[573,1555,1557],{"className":1556},[761],[573,1558,1560],{"className":1559},[766],[573,1561,1563],{"className":1562,"style":1427},[770],[573,1564,1565,1568],{"style":1430},[573,1566],{"className":1567,"style":1434},[778],[573,1569,1571],{"className":1570},[783,784,785,786],[573,1572,869],{"className":1573},[616,786],[573,1575],{"className":1576,"style":732},[731],[573,1578,703],{"className":1579},[736],[573,1581],{"className":1582,"style":732},[731],[573,1584,1586,1589,1592,1595,1598,1630,1633,1636],{"className":1585},[607],[573,1587],{"className":1588,"style":1427},[611],[573,1590,1236],{"className":1591},[616],[573,1593,861],{"className":1594,"style":961},[616,617],[573,1596],{"className":1597,"style":1148},[731],[573,1599,1601,1607],{"className":1600},[616],[573,1602,1604],{"className":1603},[616,1152],[573,1605,1111],{"className":1606},[616],[573,1608,1610],{"className":1609},[971],[573,1611,1613],{"className":1612},[761],[573,1614,1616],{"className":1615},[766],[573,1617,1619],{"className":1618,"style":1427},[770],[573,1620,1621,1624],{"style":1430},[573,1622],{"className":1623,"style":1434},[778],[573,1625,1627],{"className":1626},[783,784,785,786],[573,1628,869],{"className":1629},[616,786],[573,1631],{"className":1632,"style":732},[731],[573,1634,1249],{"className":1635},[736],[573,1637],{"className":1638,"style":732},[731],[573,1640,1642,1646,1650,1658,1662,1665],{"className":1641},[607],[573,1643],{"className":1644,"style":1645},[611],"height:1.0585em;vertical-align:-0.1944em;",[573,1647,1649],{"className":1648},[616],"113",[573,1651,1653],{"className":1652},[616],[573,1654,1657],{"className":1655},[1656],"mpunct",",",[573,1659,1661],{"className":1660},[616],"10",[573,1663],{"className":1664,"style":1148},[731],[573,1666,1668,1674],{"className":1667},[616],[573,1669,1671],{"className":1670},[616,1152],[573,1672,1111],{"className":1673},[616],[573,1675,1677],{"className":1676},[971],[573,1678,1680],{"className":1679},[761],[573,1681,1683],{"className":1682},[766],[573,1684,1686],{"className":1685,"style":1427},[770],[573,1687,1688,1691],{"style":1430},[573,1689],{"className":1690,"style":1434},[778],[573,1692,1694],{"className":1693},[783,784,785,786],[573,1695,869],{"className":1696},[616,786],[564,1698,1699,1700,1743,1744,1156],{},"Ein Fußball hat etwa den Durchmesser ",[573,1701,1703,1722],{"className":1702},[576],[573,1704,1706],{"className":1705},[580],[582,1707,1708],{"xmlns":584},[586,1709,1710,1719],{},[589,1711,1712,1715,1717],{},[710,1713,1714],{},"22",[1106,1716,1108],{},[1106,1718,1111],{},[596,1720,1721],{"encoding":598},"22\\,\\text{cm}",[573,1723,1725],{"className":1724,"ariaHidden":603},[602],[573,1726,1728,1731,1734,1737],{"className":1727},[607],[573,1729],{"className":1730,"style":1072},[611],[573,1732,1714],{"className":1733},[616],[573,1735],{"className":1736,"style":1148},[731],[573,1738,1740],{"className":1739},[616,1152],[573,1741,1111],{"className":1742},[616],", also ",[573,1745,1747,1770],{"className":1746},[576],[573,1748,1750],{"className":1749},[580],[582,1751,1752],{"xmlns":584},[586,1753,1754,1767],{},[589,1755,1756,1758,1760,1763,1765],{},[592,1757,594],{},[701,1759,703],{},[710,1761,1762],{},"11",[1106,1764,1108],{},[1106,1766,1111],{},[596,1768,1769],{"encoding":598},"r = 11\\,\\text{cm}",[573,1771,1773,1791],{"className":1772,"ariaHidden":603},[602],[573,1774,1776,1779,1782,1785,1788],{"className":1775},[607],[573,1777],{"className":1778,"style":612},[611],[573,1780,594],{"className":1781,"style":618},[616,617],[573,1783],{"className":1784,"style":732},[731],[573,1786,703],{"className":1787},[736],[573,1789],{"className":1790,"style":732},[731],[573,1792,1794,1797,1800,1803],{"className":1793},[607],[573,1795],{"className":1796,"style":1072},[611],[573,1798,1762],{"className":1799},[616],[573,1801],{"className":1802,"style":1148},[731],[573,1804,1806],{"className":1805},[616,1152],[573,1807,1111],{"className":1808},[616],[573,1810,1812],{"className":1811},[1160],[573,1813,1815,1891],{"className":1814},[576],[573,1816,1818],{"className":1817},[580],[582,1819,1820],{"xmlns":584,"display":1169},[586,1821,1822,1888],{},[589,1823,1824,1826,1828,1834,1836,1838,1840,1842,1844,1846,1848,1854,1856,1867,1869,1875,1877,1880,1882],{},[592,1825,852],{},[701,1827,703],{},[705,1829,1830,1832],{},[710,1831,1182],{},[710,1833,869],{},[701,1835,1187],{},[592,1837,861],{},[701,1839,1187],{},[701,1841,1195],{"stretchy":1194},[710,1843,1762],{},[1106,1845,1108],{},[1106,1847,1111],{},[863,1849,1850,1852],{},[701,1851,1206],{"stretchy":1194},[710,1853,869],{},[701,1855,703],{},[705,1857,1858,1865],{},[589,1859,1860,1863],{},[710,1861,1862],{},"5324",[592,1864,861],{},[710,1866,869],{},[1106,1868,1108],{},[863,1870,1871,1873],{},[1106,1872,1111],{},[710,1874,869],{},[701,1876,1249],{},[710,1878,1879],{},"5575",[1106,1881,1108],{},[863,1883,1884,1886],{},[1106,1885,1111],{},[710,1887,869],{},[596,1889,1890],{"encoding":598},"V = \\frac{4}{3} \\cdot \\pi \\cdot (11\\,\\text{cm})^3 = \\frac{5324\\pi}{3}\\,\\text{cm}^3 \\approx 5575\\,\\text{cm}^3",[573,1892,1894,1912,1989,2007,2066,2181],{"className":1893,"ariaHidden":603},[602],[573,1895,1897,1900,1903,1906,1909],{"className":1896},[607],[573,1898],{"className":1899,"style":885},[611],[573,1901,852],{"className":1902,"style":889},[616,617],[573,1904],{"className":1905,"style":732},[731],[573,1907,703],{"className":1908},[736],[573,1910],{"className":1911,"style":732},[731],[573,1913,1915,1918,1980,1983,1986],{"className":1914},[607],[573,1916],{"className":1917,"style":1291},[611],[573,1919,1921,1924,1977],{"className":1920},[616],[573,1922],{"className":1923},[753,754],[573,1925,1927],{"className":1926},[705],[573,1928,1930,1969],{"className":1929},[761,762],[573,1931,1933,1966],{"className":1932},[766],[573,1934,1936,1947,1955],{"className":1935,"style":1310},[770],[573,1937,1938,1941],{"style":1313},[573,1939],{"className":1940,"style":779},[778],[573,1942,1944],{"className":1943},[616],[573,1945,869],{"className":1946},[616],[573,1948,1949,1952],{"style":795},[573,1950],{"className":1951,"style":779},[778],[573,1953],{"className":1954,"style":803},[802],[573,1956,1957,1960],{"style":1333},[573,1958],{"className":1959,"style":779},[778],[573,1961,1963],{"className":1962},[616],[573,1964,1182],{"className":1965},[616],[573,1967,823],{"className":1968},[822],[573,1970,1972],{"className":1971},[766],[573,1973,1975],{"className":1974,"style":1352},[770],[573,1976],{},[573,1978],{"className":1979},[836,754],[573,1981],{"className":1982,"style":889},[731],[573,1984,1187],{"className":1985},[1364],[573,1987],{"className":1988,"style":889},[731],[573,1990,1992,1995,1998,2001,2004],{"className":1991},[607],[573,1993],{"className":1994,"style":1374},[611],[573,1996,861],{"className":1997,"style":961},[616,617],[573,1999],{"className":2000,"style":889},[731],[573,2002,1187],{"className":2003},[1364],[573,2005],{"className":2006,"style":889},[731],[573,2008,2010,2013,2016,2019,2022,2028,2057,2060,2063],{"className":2009},[607],[573,2011],{"className":2012,"style":1393},[611],[573,2014,1195],{"className":2015},[753],[573,2017,1762],{"className":2018},[616],[573,2020],{"className":2021,"style":1148},[731],[573,2023,2025],{"className":2024},[616,1152],[573,2026,1111],{"className":2027},[616],[573,2029,2031,2034],{"className":2030},[836],[573,2032,1206],{"className":2033},[836],[573,2035,2037],{"className":2036},[971],[573,2038,2040],{"className":2039},[761],[573,2041,2043],{"className":2042},[766],[573,2044,2046],{"className":2045,"style":1427},[770],[573,2047,2048,2051],{"style":1430},[573,2049],{"className":2050,"style":1434},[778],[573,2052,2054],{"className":2053},[783,784,785,786],[573,2055,869],{"className":2056},[616,786],[573,2058],{"className":2059,"style":732},[731],[573,2061,703],{"className":2062},[736],[573,2064],{"className":2065,"style":732},[731],[573,2067,2069,2072,2137,2140,2172,2175,2178],{"className":2068},[607],[573,2070],{"className":2071,"style":1291},[611],[573,2073,2075,2078,2134],{"className":2074},[616],[573,2076],{"className":2077},[753,754],[573,2079,2081],{"className":2080},[705],[573,2082,2084,2126],{"className":2083},[761,762],[573,2085,2087,2123],{"className":2086},[766],[573,2088,2090,2101,2109],{"className":2089,"style":1310},[770],[573,2091,2092,2095],{"style":1313},[573,2093],{"className":2094,"style":779},[778],[573,2096,2098],{"className":2097},[616],[573,2099,869],{"className":2100},[616],[573,2102,2103,2106],{"style":795},[573,2104],{"className":2105,"style":779},[778],[573,2107],{"className":2108,"style":803},[802],[573,2110,2111,2114],{"style":1333},[573,2112],{"className":2113,"style":779},[778],[573,2115,2117,2120],{"className":2116},[616],[573,2118,1862],{"className":2119},[616],[573,2121,861],{"className":2122,"style":961},[616,617],[573,2124,823],{"className":2125},[822],[573,2127,2129],{"className":2128},[766],[573,2130,2132],{"className":2131,"style":1352},[770],[573,2133],{},[573,2135],{"className":2136},[836,754],[573,2138],{"className":2139,"style":1148},[731],[573,2141,2143,2149],{"className":2142},[616],[573,2144,2146],{"className":2145},[616,1152],[573,2147,1111],{"className":2148},[616],[573,2150,2152],{"className":2151},[971],[573,2153,2155],{"className":2154},[761],[573,2156,2158],{"className":2157},[766],[573,2159,2161],{"className":2160,"style":1427},[770],[573,2162,2163,2166],{"style":1430},[573,2164],{"className":2165,"style":1434},[778],[573,2167,2169],{"className":2168},[783,784,785,786],[573,2170,869],{"className":2171},[616,786],[573,2173],{"className":2174,"style":732},[731],[573,2176,1249],{"className":2177},[736],[573,2179],{"className":2180,"style":732},[731],[573,2182,2184,2187,2190,2193],{"className":2183},[607],[573,2185],{"className":2186,"style":1427},[611],[573,2188,1879],{"className":2189},[616],[573,2191],{"className":2192,"style":1148},[731],[573,2194,2196,2202],{"className":2195},[616],[573,2197,2199],{"className":2198},[616,1152],[573,2200,1111],{"className":2201},[616],[573,2203,2205],{"className":2204},[971],[573,2206,2208],{"className":2207},[761],[573,2209,2211],{"className":2210},[766],[573,2212,2214],{"className":2213,"style":1427},[770],[573,2215,2216,2219],{"style":1430},[573,2217],{"className":2218,"style":1434},[778],[573,2220,2222],{"className":2221},[783,784,785,786],[573,2223,869],{"className":2224},[616,786],[564,2226,2227,2228,2269],{},"Das sind gut ",[573,2229,2231,2246],{"className":2230},[576],[573,2232,2234],{"className":2233},[580],[582,2235,2236],{"xmlns":584},[586,2237,2238,2243],{},[589,2239,2240],{},[710,2241,2242],{},"5,5",[596,2244,2245],{"encoding":598},"5{,}5",[573,2247,2249],{"className":2248,"ariaHidden":603},[602],[573,2250,2252,2256,2260,2266],{"className":2251},[607],[573,2253],{"className":2254,"style":2255},[611],"height:0.8389em;vertical-align:-0.1944em;",[573,2257,2259],{"className":2258},[616],"5",[573,2261,2263],{"className":2262},[616],[573,2264,1657],{"className":2265},[1656],[573,2267,2259],{"className":2268},[616]," Liter.",[559,2271,2273],{"id":2272},"typische-fehler","Typische Fehler",[2275,2276,2277,2402,2405],"ul",{},[2278,2279,2280,2341,2342,2401],"li",{},[573,2281,2283,2301],{"className":2282},[576],[573,2284,2286],{"className":2285},[580],[582,2287,2288],{"xmlns":584},[586,2289,2290,2298],{},[589,2291,2292],{},[863,2293,2294,2296],{},[592,2295,594],{},[710,2297,712],{},[596,2299,2300],{"encoding":598},"r^2",[573,2302,2304],{"className":2303,"ariaHidden":603},[602],[573,2305,2307,2311],{"className":2306},[607],[573,2308],{"className":2309,"style":2310},[611],"height:0.8141em;",[573,2312,2314,2317],{"className":2313},[616],[573,2315,594],{"className":2316,"style":618},[616,617],[573,2318,2320],{"className":2319},[971],[573,2321,2323],{"className":2322},[761],[573,2324,2326],{"className":2325},[766],[573,2327,2329],{"className":2328,"style":2310},[770],[573,2330,2332,2335],{"style":2331},"top:-3.063em;margin-right:0.05em;",[573,2333],{"className":2334,"style":1434},[778],[573,2336,2338],{"className":2337},[783,784,785,786],[573,2339,712],{"className":2340},[616,786]," statt ",[573,2343,2345,2363],{"className":2344},[576],[573,2346,2348],{"className":2347},[580],[582,2349,2350],{"xmlns":584},[586,2351,2352,2360],{},[589,2353,2354],{},[863,2355,2356,2358],{},[592,2357,594],{},[710,2359,869],{},[596,2361,2362],{"encoding":598},"r^3",[573,2364,2366],{"className":2365,"ariaHidden":603},[602],[573,2367,2369,2372],{"className":2368},[607],[573,2370],{"className":2371,"style":2310},[611],[573,2373,2375,2378],{"className":2374},[616],[573,2376,594],{"className":2377,"style":618},[616,617],[573,2379,2381],{"className":2380},[971],[573,2382,2384],{"className":2383},[761],[573,2385,2387],{"className":2386},[766],[573,2388,2390],{"className":2389,"style":2310},[770],[573,2391,2392,2395],{"style":2331},[573,2393],{"className":2394,"style":1434},[778],[573,2396,2398],{"className":2397},[783,784,785,786],[573,2399,869],{"className":2400},[616,786]," nehmen. Das Volumen hat drei Längen-Dimensionen, deshalb hoch 3.",[2278,2403,2404],{},"Den Durchmesser statt des Radius einsetzen. Das ergibt das achtfache Volumen.",[2278,2406,2407,2408,1011],{},"Volumen und Oberfläche verwechseln. Die Oberfläche ist ",[573,2409,2411,2438],{"className":2410},[576],[573,2412,2414],{"className":2413},[580],[582,2415,2416],{"xmlns":584},[586,2417,2418,2435],{},[589,2419,2420,2423,2425,2427,2429],{},[592,2421,2422],{},"O",[701,2424,703],{},[710,2426,1182],{},[592,2428,861],{},[863,2430,2431,2433],{},[592,2432,594],{},[710,2434,712],{},[596,2436,2437],{"encoding":598},"O = 4\\pi r^2",[573,2439,2441,2459],{"className":2440,"ariaHidden":603},[602],[573,2442,2444,2447,2450,2453,2456],{"className":2443},[607],[573,2445],{"className":2446,"style":885},[611],[573,2448,2422],{"className":2449,"style":618},[616,617],[573,2451],{"className":2452,"style":732},[731],[573,2454,703],{"className":2455},[736],[573,2457],{"className":2458,"style":732},[731],[573,2460,2462,2465,2468,2471],{"className":2461},[607],[573,2463],{"className":2464,"style":2310},[611],[573,2466,1182],{"className":2467},[616],[573,2469,861],{"className":2470,"style":961},[616,617],[573,2472,2474,2477],{"className":2473},[616],[573,2475,594],{"className":2476,"style":618},[616,617],[573,2478,2480],{"className":2479},[971],[573,2481,2483],{"className":2482},[761],[573,2484,2486],{"className":2485},[766],[573,2487,2489],{"className":2488,"style":2310},[770],[573,2490,2491,2494],{"style":2331},[573,2492],{"className":2493,"style":1434},[778],[573,2495,2497],{"className":2496},[783,784,785,786],[573,2498,712],{"className":2499},[616,786],{"title":2501,"searchDepth":2502,"depth":2502,"links":2503},"",2,[2504,2505,2506],{"id":561,"depth":2502,"text":562},{"id":1082,"depth":2502,"text":1083},{"id":2272,"depth":2502,"text":2273},[2508,2511,2513,2516,2519,2522],{"lhs":2509,"rhs":2510},"4\u002F3 * pi * r^3","pi * (2*r)^3 \u002F 6",{"lhs":2512,"rhs":2509},"pi*r^2*(2*r) - 2 * (1\u002F3*pi*r^2*r)",{"lhs":2514,"rhs":2515},"4\u002F3 * pi * 3^3","36 * pi",{"lhs":2517,"rhs":2518},"round(36 * pi, 2)","113.1",{"lhs":2520,"rhs":2521},"4\u002F3 * pi * 11^3","5324 * pi \u002F 3",{"lhs":2523,"rhs":1879},"round(5324 * pi \u002F 3)",null,"md",{"caption":2527,"x":2528,"y":2531,"items":2532},"Kugel mit dem Mittelpunkt M und dem Radius r",[2529,2530],-2.45,2.45,[2529,2530],[2533,2538,2543,2547,2551,2558,2563],{"type":2534,"center":2535,"rx":2502,"ry":2502,"fill":2537},"ellipse",[2536,2536],0,true,{"type":2534,"center":2539,"rx":2502,"ry":2540,"start":2536,"end":2541,"style":2542},[2536,2536],0.6,180,"dashed",{"type":2534,"center":2544,"rx":2502,"ry":2540,"start":2541,"end":2545,"style":2546},[2536,2536],360,"muted",{"type":2548,"from":2549,"to":2550},"segment",[2536,2536],[2502,2536],{"type":2552,"at":2553,"label":2554,"offset":2555},"point",[2536,2536],"M",[2556,2557],-6,16,{"type":2559,"at":2560,"text":594},"label",[2561,2562],1,0.22,{"type":2559,"at":2564,"text":852},[2565,2566],-0.8,1.2,"\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\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-sphere-volume-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-sphere-volume-clip\">\u003Crect x=\"0\" y=\"0\" width=\"235.2\" height=\"235.2\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cellipse cx=\"117.6\" cy=\"117.6\" rx=\"96\" ry=\"96\" class=\"fig-main fig-fill\"\u002F>\u003Cpath d=\"M 213.6 117.6 A 96 28.8 0 0 0 21.6 117.6\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 21.6 117.6 A 96 28.8 0 0 0 213.6 117.6\" class=\"fig-muted\"\u002F>\u003Cline x1=\"117.6\" y1=\"117.6\" x2=\"213.6\" y2=\"117.6\" class=\"fig-main\"\u002F>\u003Ccircle cx=\"117.6\" cy=\"117.6\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"111.6\" y=\"133.6\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">M\u003C\u002Ftext>\u003Ctext x=\"165.6\" y=\"107.04\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003C\u002Ftext>\u003Ctext x=\"79.2\" y=\"60\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">V\u003C\u002Ftext>\u003C\u002Fsvg>","sphere-volume","V = \\frac{4}{3} \\pi r^3","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>4\u003C\u002Fmn>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmi>π\u003C\u002Fmi>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V = \\frac{4}{3} \\pi r^3\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">4\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"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\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-kugel",[],[2576,2577,2578],"sphere-surface","cylinder-volume","cone-volume",{"title":548,"description":2501},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-kugel","Das Volumen einer Kugel ist vier Drittel mal π mal Radius hoch 3.",[2583,2584,2585,2586],"volumen","kugel","radius","körper",[2588,2591,2594],{"symbol":852,"meaning":2589,"symbolHtml":2590},"Volumen der Kugel","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":594,"meaning":2592,"symbolHtml":2593},"Radius der Kugel, der Abstand vom Mittelpunkt zur Oberfläche","\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":2595,"meaning":2596,"symbolHtml":2597},"\\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>","fNSylY3tW2bSA-OQNQb3xO9vUrdkG2lHDIYFi_bSLfQ",[2600,2603,2606],{"stem":2601,"title":2602,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-kugel","Oberfläche einer Kugel",{"stem":2604,"title":2605,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-kegel","Volumen eines Kegels",{"stem":2607,"title":2608,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fvolumen-zylinder","Volumen eines Zylinders",1793824270545]