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10\\,\\text{cm}",[580,1099,1101,1119],{"className":1100,"ariaHidden":628},[627],[580,1102,1104,1107,1110,1113,1116],{"className":1103},[632],[580,1105],{"className":1106,"style":818},[636],[580,1108,738],{"className":1109},[641,642],[580,1111],{"className":1112,"style":647},[646],[580,1114,605],{"className":1115},[651],[580,1117],{"className":1118,"style":647},[646],[580,1120,1122,1125,1128,1131],{"className":1121},[632],[580,1123],{"className":1124,"style":1056},[636],[580,1126,1090],{"className":1127},[641],[580,1129],{"className":1130,"style":1063},[646],[580,1132,1134],{"className":1133},[641,1067],[580,1135,1025],{"className":1136},[641],":",[580,1139,1142],{"className":1140},[1141],"katex-display",[580,1143,1145,1220],{"className":1144},[583],[580,1146,1148],{"className":1147},[587],[589,1149,1151],{"xmlns":591,"display":1150},"block",[593,1152,1153,1217],{},[596,1154,1155,1157,1159,1161,1163,1167,1169,1171,1173,1180,1182,1184,1186,1188,1190,1193,1195,1197,1203,1206,1209,1211],{},[599,1156,722],{},[603,1158,605],{},[599,1160,608],{},[603,1162,735],{},[603,1164,1166],{"stretchy":1165},"false","(",[616,1168,1018],{},[1020,1170,1022],{},[1020,1172,1025],{},[610,1174,1175,1178],{},[603,1176,1177],{"stretchy":1165},")",[616,1179,618],{},[603,1181,735],{},[616,1183,1090],{},[1020,1185,1022],{},[1020,1187,1025],{},[603,1189,605],{},[616,1191,1192],{},"90",[599,1194,608],{},[1020,1196,1022],{},[610,1198,1199,1201],{},[1020,1200,1025],{},[616,1202,1018],{},[603,1204,1205],{},"≈",[616,1207,1208],{},"282,74",[1020,1210,1022],{},[610,1212,1213,1215],{},[1020,1214,1025],{},[616,1216,1018],{},[620,1218,1219],{"encoding":622},"V = \\pi \\cdot (3\\,\\text{cm})^2 \\cdot 10\\,\\text{cm} = 90\\pi\\,\\text{cm}^3 \\approx 282{,}74\\,\\text{cm}^3",[580,1221,1223,1241,1260,1322,1349,1405],{"className":1222,"ariaHidden":628},[627],[580,1224,1226,1229,1232,1235,1238],{"className":1225},[632],[580,1227],{"className":1228,"style":637},[636],[580,1230,722],{"className":1231,"style":754},[641,642],[580,1233],{"className":1234,"style":647},[646],[580,1236,605],{"className":1237},[651],[580,1239],{"className":1240,"style":647},[646],[580,1242,1244,1248,1251,1254,1257],{"className":1243},[632],[580,1245],{"className":1246,"style":1247},[636],"height:0.4445em;",[580,1249,608],{"className":1250,"style":665},[641,642],[580,1252],{"className":1253,"style":754},[646],[580,1255,735],{"className":1256},[808],[580,1258],{"className":1259,"style":754},[646],[580,1261,1263,1267,1270,1273,1276,1282,1313,1316,1319],{"className":1262},[632],[580,1264],{"className":1265,"style":1266},[636],"height:1.1141em;vertical-align:-0.25em;",[580,1268,1166],{"className":1269},[917],[580,1271,1018],{"className":1272},[641],[580,1274],{"className":1275,"style":1063},[646],[580,1277,1279],{"className":1278},[641,1067],[580,1280,1025],{"className":1281},[641],[580,1283,1285,1288],{"className":1284},[992],[580,1286,1177],{"className":1287},[992],[580,1289,1291],{"className":1290},[676],[580,1292,1294],{"className":1293},[680],[580,1295,1297],{"className":1296},[684],[580,1298,1301],{"className":1299,"style":1300},[688],"height:0.8641em;",[580,1302,1304,1307],{"style":1303},"top:-3.113em;margin-right:0.05em;",[580,1305],{"className":1306,"style":696},[695],[580,1308,1310],{"className":1309},[700,701,702,703],[580,1311,618],{"className":1312},[641,703],[580,1314],{"className":1315,"style":754},[646],[580,1317,735],{"className":1318},[808],[580,1320],{"className":1321,"style":754},[646],[580,1323,1325,1328,1331,1334,1340,1343,1346],{"className":1324},[632],[580,1326],{"className":1327,"style":1056},[636],[580,1329,1090],{"className":1330},[641],[580,1332],{"className":1333,"style":1063},[646],[580,1335,1337],{"className":1336},[641,1067],[580,1338,1025],{"className":1339},[641],[580,1341],{"className":1342,"style":647},[646],[580,1344,605],{"className":1345},[651],[580,1347],{"className":1348,"style":647},[646],[580,1350,1352,1355,1358,1361,1364,1396,1399,1402],{"className":1351},[632],[580,1353],{"className":1354,"style":1300},[636],[580,1356,1192],{"className":1357},[641],[580,1359,608],{"className":1360,"style":665},[641,642],[580,1362],{"className":1363,"style":1063},[646],[580,1365,1367,1373],{"className":1366},[641],[580,1368,1370],{"className":1369},[641,1067],[580,1371,1025],{"className":1372},[641],[580,1374,1376],{"className":1375},[676],[580,1377,1379],{"className":1378},[680],[580,1380,1382],{"className":1381},[684],[580,1383,1385],{"className":1384,"style":1300},[688],[580,1386,1387,1390],{"style":1303},[580,1388],{"className":1389,"style":696},[695],[580,1391,1393],{"className":1392},[700,701,702,703],[580,1394,1018],{"className":1395},[641,703],[580,1397],{"className":1398,"style":647},[646],[580,1400,1205],{"className":1401},[651],[580,1403],{"className":1404,"style":647},[646],[580,1406,1408,1412,1416,1424,1428,1431],{"className":1407},[632],[580,1409],{"className":1410,"style":1411},[636],"height:1.0585em;vertical-align:-0.1944em;",[580,1413,1415],{"className":1414},[641],"282",[580,1417,1419],{"className":1418},[641],[580,1420,1423],{"className":1421},[1422],"mpunct",",",[580,1425,1427],{"className":1426},[641],"74",[580,1429],{"className":1430,"style":1063},[646],[580,1432,1434,1440],{"className":1433},[641],[580,1435,1437],{"className":1436},[641,1067],[580,1438,1025],{"className":1439},[641],[580,1441,1443],{"className":1442},[676],[580,1444,1446],{"className":1445},[680],[580,1447,1449],{"className":1448},[684],[580,1450,1452],{"className":1451,"style":1300},[688],[580,1453,1454,1457],{"style":1303},[580,1455],{"className":1456,"style":696},[695],[580,1458,1460],{"className":1459},[700,701,702,703],[580,1461,1018],{"className":1462},[641,703],[564,1464,1465,1466,1509,1510,707,1553,1137],{},"Eine Dose ist ",[580,1467,1469,1488],{"className":1468},[583],[580,1470,1472],{"className":1471},[587],[589,1473,1474],{"xmlns":591},[593,1475,1476,1485],{},[596,1477,1478,1481,1483],{},[616,1479,1480],{},"12",[1020,1482,1022],{},[1020,1484,1025],{},[620,1486,1487],{"encoding":622},"12\\,\\text{cm}",[580,1489,1491],{"className":1490,"ariaHidden":628},[627],[580,1492,1494,1497,1500,1503],{"className":1493},[632],[580,1495],{"className":1496,"style":1056},[636],[580,1498,1480],{"className":1499},[641],[580,1501],{"className":1502,"style":1063},[646],[580,1504,1506],{"className":1505},[641,1067],[580,1507,1025],{"className":1508},[641]," hoch und hat den Durchmesser ",[580,1511,1513,1532],{"className":1512},[583],[580,1514,1516],{"className":1515},[587],[589,1517,1518],{"xmlns":591},[593,1519,1520,1529],{},[596,1521,1522,1525,1527],{},[616,1523,1524],{},"8",[1020,1526,1022],{},[1020,1528,1025],{},[620,1530,1531],{"encoding":622},"8\\,\\text{cm}",[580,1533,1535],{"className":1534,"ariaHidden":628},[627],[580,1536,1538,1541,1544,1547],{"className":1537},[632],[580,1539],{"className":1540,"style":1056},[636],[580,1542,1524],{"className":1543},[641],[580,1545],{"className":1546,"style":1063},[646],[580,1548,1550],{"className":1549},[641,1067],[580,1551,1025],{"className":1552},[641],[580,1554,1556,1579],{"className":1555},[583],[580,1557,1559],{"className":1558},[587],[589,1560,1561],{"xmlns":591},[593,1562,1563,1576],{},[596,1564,1565,1567,1569,1572,1574],{},[599,1566,614],{},[603,1568,605],{},[616,1570,1571],{},"4",[1020,1573,1022],{},[1020,1575,1025],{},[620,1577,1578],{"encoding":622},"r = 4\\,\\text{cm}",[580,1580,1582,1600],{"className":1581,"ariaHidden":628},[627],[580,1583,1585,1588,1591,1594,1597],{"className":1584},[632],[580,1586],{"className":1587,"style":891},[636],[580,1589,614],{"className":1590,"style":672},[641,642],[580,1592],{"className":1593,"style":647},[646],[580,1595,605],{"className":1596},[651],[580,1598],{"className":1599,"style":647},[646],[580,1601,1603,1606,1609,1612],{"className":1602},[632],[580,1604],{"className":1605,"style":1056},[636],[580,1607,1571],{"className":1608},[641],[580,1610],{"className":1611,"style":1063},[646],[580,1613,1615],{"className":1614},[641,1067],[580,1616,1025],{"className":1617},[641],[580,1619,1621],{"className":1620},[1141],[580,1622,1624,1694],{"className":1623},[583],[580,1625,1627],{"className":1626},[587],[589,1628,1629],{"xmlns":591,"display":1150},[593,1630,1631,1691],{},[596,1632,1633,1635,1637,1639,1641,1643,1645,1647,1649,1655,1657,1659,1661,1663,1665,1668,1670,1672,1678,1680,1683,1685],{},[599,1634,722],{},[603,1636,605],{},[599,1638,608],{},[603,1640,735],{},[603,1642,1166],{"stretchy":1165},[616,1644,1571],{},[1020,1646,1022],{},[1020,1648,1025],{},[610,1650,1651,1653],{},[603,1652,1177],{"stretchy":1165},[616,1654,618],{},[603,1656,735],{},[616,1658,1480],{},[1020,1660,1022],{},[1020,1662,1025],{},[603,1664,605],{},[616,1666,1667],{},"192",[599,1669,608],{},[1020,1671,1022],{},[610,1673,1674,1676],{},[1020,1675,1025],{},[616,1677,1018],{},[603,1679,1205],{},[616,1681,1682],{},"603,19",[1020,1684,1022],{},[610,1686,1687,1689],{},[1020,1688,1025],{},[616,1690,1018],{},[620,1692,1693],{"encoding":622},"V = \\pi \\cdot (4\\,\\text{cm})^2 \\cdot 12\\,\\text{cm} = 192\\pi\\,\\text{cm}^3 \\approx 603{,}19\\,\\text{cm}^3",[580,1695,1697,1715,1733,1792,1819,1875],{"className":1696,"ariaHidden":628},[627],[580,1698,1700,1703,1706,1709,1712],{"className":1699},[632],[580,1701],{"className":1702,"style":637},[636],[580,1704,722],{"className":1705,"style":754},[641,642],[580,1707],{"className":1708,"style":647},[646],[580,1710,605],{"className":1711},[651],[580,1713],{"className":1714,"style":647},[646],[580,1716,1718,1721,1724,1727,1730],{"className":1717},[632],[580,1719],{"className":1720,"style":1247},[636],[580,1722,608],{"className":1723,"style":665},[641,642],[580,1725],{"className":1726,"style":754},[646],[580,1728,735],{"className":1729},[808],[580,1731],{"className":1732,"style":754},[646],[580,1734,1736,1739,1742,1745,1748,1754,1783,1786,1789],{"className":1735},[632],[580,1737],{"className":1738,"style":1266},[636],[580,1740,1166],{"className":1741},[917],[580,1743,1571],{"className":1744},[641],[580,1746],{"className":1747,"style":1063},[646],[580,1749,1751],{"className":1750},[641,1067],[580,1752,1025],{"className":1753},[641],[580,1755,1757,1760],{"className":1756},[992],[580,1758,1177],{"className":1759},[992],[580,1761,1763],{"className":1762},[676],[580,1764,1766],{"className":1765},[680],[580,1767,1769],{"className":1768},[684],[580,1770,1772],{"className":1771,"style":1300},[688],[580,1773,1774,1777],{"style":1303},[580,1775],{"className":1776,"style":696},[695],[580,1778,1780],{"className":1779},[700,701,702,703],[580,1781,618],{"className":1782},[641,703],[580,1784],{"className":1785,"style":754},[646],[580,1787,735],{"className":1788},[808],[580,1790],{"className":1791,"style":754},[646],[580,1793,1795,1798,1801,1804,1810,1813,1816],{"className":1794},[632],[580,1796],{"className":1797,"style":1056},[636],[580,1799,1480],{"className":1800},[641],[580,1802],{"className":1803,"style":1063},[646],[580,1805,1807],{"className":1806},[641,1067],[580,1808,1025],{"className":1809},[641],[580,1811],{"className":1812,"style":647},[646],[580,1814,605],{"className":1815},[651],[580,1817],{"className":1818,"style":647},[646],[580,1820,1822,1825,1828,1831,1834,1866,1869,1872],{"className":1821},[632],[580,1823],{"className":1824,"style":1300},[636],[580,1826,1667],{"className":1827},[641],[580,1829,608],{"className":1830,"style":665},[641,642],[580,1832],{"className":1833,"style":1063},[646],[580,1835,1837,1843],{"className":1836},[641],[580,1838,1840],{"className":1839},[641,1067],[580,1841,1025],{"className":1842},[641],[580,1844,1846],{"className":1845},[676],[580,1847,1849],{"className":1848},[680],[580,1850,1852],{"className":1851},[684],[580,1853,1855],{"className":1854,"style":1300},[688],[580,1856,1857,1860],{"style":1303},[580,1858],{"className":1859,"style":696},[695],[580,1861,1863],{"className":1862},[700,701,702,703],[580,1864,1018],{"className":1865},[641,703],[580,1867],{"className":1868,"style":647},[646],[580,1870,1205],{"className":1871},[651],[580,1873],{"className":1874,"style":647},[646],[580,1876,1878,1881,1885,1891,1895,1898],{"className":1877},[632],[580,1879],{"className":1880,"style":1411},[636],[580,1882,1884],{"className":1883},[641],"603",[580,1886,1888],{"className":1887},[641],[580,1889,1423],{"className":1890},[1422],[580,1892,1894],{"className":1893},[641],"19",[580,1896],{"className":1897,"style":1063},[646],[580,1899,1901,1907],{"className":1900},[641],[580,1902,1904],{"className":1903},[641,1067],[580,1905,1025],{"className":1906},[641],[580,1908,1910],{"className":1909},[676],[580,1911,1913],{"className":1912},[680],[580,1914,1916],{"className":1915},[684],[580,1917,1919],{"className":1918,"style":1300},[688],[580,1920,1921,1924],{"style":1303},[580,1922],{"className":1923,"style":696},[695],[580,1925,1927],{"className":1926},[700,701,702,703],[580,1928,1018],{"className":1929},[641,703],[564,1931,1932,1933,1975],{},"Das sind etwa ",[580,1934,1936,1951],{"className":1935},[583],[580,1937,1939],{"className":1938},[587],[589,1940,1941],{"xmlns":591},[593,1942,1943,1948],{},[596,1944,1945],{},[616,1946,1947],{},"0,6",[620,1949,1950],{"encoding":622},"0{,}6",[580,1952,1954],{"className":1953,"ariaHidden":628},[627],[580,1955,1957,1961,1965,1971],{"className":1956},[632],[580,1958],{"className":1959,"style":1960},[636],"height:0.8389em;vertical-align:-0.1944em;",[580,1962,1964],{"className":1963},[641],"0",[580,1966,1968],{"className":1967},[641],[580,1969,1423],{"className":1970},[1422],[580,1972,1974],{"className":1973},[641],"6"," Liter.",[559,1977,1979],{"id":1978},"typische-fehler","Typische Fehler",[1981,1982,1983,1987,2064],"ul",{},[1984,1985,1986],"li",{},"Den Durchmesser statt des Radius einsetzen. Das ergibt das vierfache Volumen.",[1984,1988,1989,1990,2063],{},"Den Radius nicht quadrieren: ",[580,1991,1993,2015],{"className":1992},[583],[580,1994,1996],{"className":1995},[587],[589,1997,1998],{"xmlns":591},[593,1999,2000,2012],{},[596,2001,2002,2004,2006,2008,2010],{},[599,2003,608],{},[603,2005,735],{},[599,2007,614],{},[603,2009,735],{},[599,2011,738],{},[620,2013,2014],{"encoding":622},"\\pi \\cdot r \\cdot h",[580,2016,2018,2036,2054],{"className":2017,"ariaHidden":628},[627],[580,2019,2021,2024,2027,2030,2033],{"className":2020},[632],[580,2022],{"className":2023,"style":1247},[636],[580,2025,608],{"className":2026,"style":665},[641,642],[580,2028],{"className":2029,"style":754},[646],[580,2031,735],{"className":2032},[808],[580,2034],{"className":2035,"style":754},[646],[580,2037,2039,2042,2045,2048,2051],{"className":2038},[632],[580,2040],{"className":2041,"style":1247},[636],[580,2043,614],{"className":2044,"style":672},[641,642],[580,2046],{"className":2047,"style":754},[646],[580,2049,735],{"className":2050},[808],[580,2052],{"className":2053,"style":754},[646],[580,2055,2057,2060],{"className":2056},[632],[580,2058],{"className":2059,"style":818},[636],[580,2061,738],{"className":2062},[641,642]," ist falsch.",[1984,2065,2066,2067,2168],{},"Mit dem Kegel verwechseln. Beim Kegel kommt noch der Faktor ",[580,2068,2070,2089],{"className":2069},[583],[580,2071,2073],{"className":2072},[587],[589,2074,2075],{"xmlns":591},[593,2076,2077,2086],{},[596,2078,2079],{},[873,2080,2081,2084],{},[616,2082,2083],{},"1",[616,2085,1018],{},[620,2087,2088],{"encoding":622},"\\frac{1}{3}",[580,2090,2092],{"className":2091,"ariaHidden":628},[627],[580,2093,2095,2099],{"className":2094},[632],[580,2096],{"className":2097,"style":2098},[636],"height:1.1901em;vertical-align:-0.345em;",[580,2100,2102,2105,2165],{"className":2101},[641],[580,2103],{"className":2104},[917,918],[580,2106,2108],{"className":2107},[873],[580,2109,2111,2157],{"className":2110},[680,925],[580,2112,2114,2154],{"className":2113},[684],[580,2115,2118,2132,2140],{"className":2116,"style":2117},[688],"height:0.8451em;",[580,2119,2120,2123],{"style":935},[580,2121],{"className":2122,"style":939},[695],[580,2124,2126],{"className":2125},[700,701,702,703],[580,2127,2129],{"className":2128},[641,703],[580,2130,1018],{"className":2131},[641,703],[580,2133,2134,2137],{"style":951},[580,2135],{"className":2136,"style":939},[695],[580,2138],{"className":2139,"style":959},[958],[580,2141,2142,2145],{"style":962},[580,2143],{"className":2144,"style":939},[695],[580,2146,2148],{"className":2147},[700,701,702,703],[580,2149,2151],{"className":2150},[641,703],[580,2152,2083],{"className":2153},[641,703],[580,2155,979],{"className":2156},[978],[580,2158,2160],{"className":2159},[684],[580,2161,2163],{"className":2162,"style":986},[688],[580,2164],{},[580,2166],{"className":2167},[992,918]," dazu.",{"title":2170,"searchDepth":2171,"depth":2171,"links":2172},"",2,[2173,2174,2175],{"id":561,"depth":2171,"text":562},{"id":995,"depth":2171,"text":996},{"id":1978,"depth":2171,"text":1979},[2177,2180,2183,2186],{"lhs":2178,"rhs":2179},"pi * 3^2 * 10","90 * pi",{"lhs":2181,"rhs":2182},"round(90 * pi, 2)","282.74",{"lhs":2184,"rhs":2185},"pi * (8\u002F2)^2 * 12","192 * pi",{"lhs":2187,"rhs":2188},"round(192 * pi, 2)","603.19",null,"md",{"caption":2192,"x":2193,"y":2196,"items":2199},"Zylinder mit dem Radius r der Grundfläche und der Höhe 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