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10\\,\\text{cm}",[579,1055,1057,1075],{"className":1056,"ariaHidden":622},[621],[579,1058,1060,1063,1066,1069,1072],{"className":1059},[626],[579,1061],{"className":1062,"style":752},[630],[579,1064,716],{"className":1065},[635,639],[579,1067],{"className":1068,"style":738},[737],[579,1070,707],{"className":1071},[742],[579,1073],{"className":1074,"style":738},[737],[579,1076,1078,1081,1084,1087],{"className":1077},[626],[579,1079],{"className":1080,"style":827},[630],[579,1082,1046],{"className":1083},[635],[579,1085],{"className":1086,"style":1019},[737],[579,1088,1090],{"className":1089},[635,1023],[579,1091,981],{"className":1092},[635],":",[579,1095,1098],{"className":1096},[1097],"katex-display",[579,1099,1101,1220],{"className":1100},[582],[579,1102,1104],{"className":1103},[586],[588,1105,1107],{"xmlns":590,"display":1106},"block",[592,1108,1109,1217],{},[595,1110,1111,1113,1115,1117,1119,1122,1124,1126,1128,1130,1136,1138,1140,1142,1144,1146,1148,1150,1152,1154,1156,1158,1160,1163,1165,1167,1173,1175,1178,1180,1182,1188,1190,1193,1195,1197,1203,1206,1209,1211],{},[602,1112,855],{},[705,1114,707],{},[598,1116,600],{},[602,1118,604],{},[705,1120,1121],{},"⋅",[705,1123,867],{"stretchy":866},[598,1125,974],{},[976,1127,978],{},[976,1129,981],{},[606,1131,1132,1134],{},[705,1133,877],{"stretchy":866},[598,1135,600],{},[705,1137,872],{},[598,1139,600],{},[602,1141,604],{},[705,1143,1121],{},[598,1145,974],{},[976,1147,978],{},[976,1149,981],{},[705,1151,1121],{},[598,1153,1046],{},[976,1155,978],{},[976,1157,981],{},[705,1159,707],{},[598,1161,1162],{},"18",[602,1164,604],{},[976,1166,978],{},[606,1168,1169,1171],{},[976,1170,981],{},[598,1172,600],{},[705,1174,872],{},[598,1176,1177],{},"60",[602,1179,604],{},[976,1181,978],{},[606,1183,1184,1186],{},[976,1185,981],{},[598,1187,600],{},[705,1189,707],{},[598,1191,1192],{},"78",[602,1194,604],{},[976,1196,978],{},[606,1198,1199,1201],{},[976,1200,981],{},[598,1202,600],{},[705,1204,1205],{},"≈",[598,1207,1208],{},"245,04",[976,1210,978],{},[606,1212,1213,1215],{},[976,1214,981],{},[598,1216,600],{},[614,1218,1219],{"encoding":616},"O = 2\\pi \\cdot (3\\,\\text{cm})^2 + 2\\pi \\cdot 3\\,\\text{cm} \\cdot 10\\,\\text{cm} = 18\\pi\\,\\text{cm}^2 + 60\\pi\\,\\text{cm}^2 = 78\\pi\\,\\text{cm}^2 \\approx 245{,}04\\,\\text{cm}^2",[579,1221,1223,1241,1262,1324,1345,1372,1399,1456,1512,1568],{"className":1222,"ariaHidden":622},[621],[579,1224,1226,1229,1232,1235,1238],{"className":1225},[626],[579,1227],{"className":1228,"style":729},[630],[579,1230,855],{"className":1231,"style":647},[635,639],[579,1233],{"className":1234,"style":738},[737],[579,1236,707],{"className":1237},[742],[579,1239],{"className":1240,"style":738},[737],[579,1242,1244,1247,1250,1253,1256,1259],{"className":1243},[626],[579,1245],{"className":1246,"style":827},[630],[579,1248,600],{"className":1249},[635],[579,1251,604],{"className":1252,"style":640},[635,639],[579,1254],{"className":1255,"style":928},[737],[579,1257,1121],{"className":1258},[932],[579,1260],{"className":1261,"style":928},[737],[579,1263,1265,1269,1272,1275,1278,1284,1315,1318,1321],{"className":1264},[626],[579,1266],{"className":1267,"style":1268},[630],"height:1.1141em;vertical-align:-0.25em;",[579,1270,867],{"className":1271},[921],[579,1273,974],{"className":1274},[635],[579,1276],{"className":1277,"style":1019},[737],[579,1279,1281],{"className":1280},[635,1023],[579,1282,981],{"className":1283},[635],[579,1285,1287,1290],{"className":1286},[948],[579,1288,877],{"className":1289},[948],[579,1291,1293],{"className":1292},[651],[579,1294,1296],{"className":1295},[655],[579,1297,1299],{"className":1298},[659],[579,1300,1303],{"className":1301,"style":1302},[663],"height:0.8641em;",[579,1304,1306,1309],{"style":1305},"top:-3.113em;margin-right:0.05em;",[579,1307],{"className":1308,"style":671},[670],[579,1310,1312],{"className":1311},[675,676,677,678],[579,1313,600],{"className":1314},[635,678],[579,1316],{"className":1317,"style":928},[737],[579,1319,872],{"className":1320},[932],[579,1322],{"className":1323,"style":928},[737],[579,1325,1327,1330,1333,1336,1339,1342],{"className":1326},[626],[579,1328],{"className":1329,"style":827},[630],[579,1331,600],{"className":1332},[635],[579,1334,604],{"className":1335,"style":640},[635,639],[579,1337],{"className":1338,"style":928},[737],[579,1340,1121],{"className":1341},[932],[579,1343],{"className":1344,"style":928},[737],[579,1346,1348,1351,1354,1357,1363,1366,1369],{"className":1347},[626],[579,1349],{"className":1350,"style":827},[630],[579,1352,974],{"className":1353},[635],[579,1355],{"className":1356,"style":1019},[737],[579,1358,1360],{"className":1359},[635,1023],[579,1361,981],{"className":1362},[635],[579,1364],{"className":1365,"style":928},[737],[579,1367,1121],{"className":1368},[932],[579,1370],{"className":1371,"style":928},[737],[579,1373,1375,1378,1381,1384,1390,1393,1396],{"className":1374},[626],[579,1376],{"className":1377,"style":827},[630],[579,1379,1046],{"className":1380},[635],[579,1382],{"className":1383,"style":1019},[737],[579,1385,1387],{"className":1386},[635,1023],[579,1388,981],{"className":1389},[635],[579,1391],{"className":1392,"style":738},[737],[579,1394,707],{"className":1395},[742],[579,1397],{"className":1398,"style":738},[737],[579,1400,1402,1406,1409,1412,1415,1447,1450,1453],{"className":1401},[626],[579,1403],{"className":1404,"style":1405},[630],"height:0.9474em;vertical-align:-0.0833em;",[579,1407,1162],{"className":1408},[635],[579,1410,604],{"className":1411,"style":640},[635,639],[579,1413],{"className":1414,"style":1019},[737],[579,1416,1418,1424],{"className":1417},[635],[579,1419,1421],{"className":1420},[635,1023],[579,1422,981],{"className":1423},[635],[579,1425,1427],{"className":1426},[651],[579,1428,1430],{"className":1429},[655],[579,1431,1433],{"className":1432},[659],[579,1434,1436],{"className":1435,"style":1302},[663],[579,1437,1438,1441],{"style":1305},[579,1439],{"className":1440,"style":671},[670],[579,1442,1444],{"className":1443},[675,676,677,678],[579,1445,600],{"className":1446},[635,678],[579,1448],{"className":1449,"style":928},[737],[579,1451,872],{"className":1452},[932],[579,1454],{"className":1455,"style":928},[737],[579,1457,1459,1462,1465,1468,1471,1503,1506,1509],{"className":1458},[626],[579,1460],{"className":1461,"style":1302},[630],[579,1463,1177],{"className":1464},[635],[579,1466,604],{"className":1467,"style":640},[635,639],[579,1469],{"className":1470,"style":1019},[737],[579,1472,1474,1480],{"className":1473},[635],[579,1475,1477],{"className":1476},[635,1023],[579,1478,981],{"className":1479},[635],[579,1481,1483],{"className":1482},[651],[579,1484,1486],{"className":1485},[655],[579,1487,1489],{"className":1488},[659],[579,1490,1492],{"className":1491,"style":1302},[663],[579,1493,1494,1497],{"style":1305},[579,1495],{"className":1496,"style":671},[670],[579,1498,1500],{"className":1499},[675,676,677,678],[579,1501,600],{"className":1502},[635,678],[579,1504],{"className":1505,"style":738},[737],[579,1507,707],{"className":1508},[742],[579,1510],{"className":1511,"style":738},[737],[579,1513,1515,1518,1521,1524,1527,1559,1562,1565],{"className":1514},[626],[579,1516],{"className":1517,"style":1302},[630],[579,1519,1192],{"className":1520},[635],[579,1522,604],{"className":1523,"style":640},[635,639],[579,1525],{"className":1526,"style":1019},[737],[579,1528,1530,1536],{"className":1529},[635],[579,1531,1533],{"className":1532},[635,1023],[579,1534,981],{"className":1535},[635],[579,1537,1539],{"className":1538},[651],[579,1540,1542],{"className":1541},[655],[579,1543,1545],{"className":1544},[659],[579,1546,1548],{"className":1547,"style":1302},[663],[579,1549,1550,1553],{"style":1305},[579,1551],{"className":1552,"style":671},[670],[579,1554,1556],{"className":1555},[675,676,677,678],[579,1557,600],{"className":1558},[635,678],[579,1560],{"className":1561,"style":738},[737],[579,1563,1205],{"className":1564},[742],[579,1566],{"className":1567,"style":738},[737],[579,1569,1571,1575,1579,1587,1591,1594],{"className":1570},[626],[579,1572],{"className":1573,"style":1574},[630],"height:1.0585em;vertical-align:-0.1944em;",[579,1576,1578],{"className":1577},[635],"245",[579,1580,1582],{"className":1581},[635],[579,1583,1586],{"className":1584},[1585],"mpunct",",",[579,1588,1590],{"className":1589},[635],"04",[579,1592],{"className":1593,"style":1019},[737],[579,1595,1597,1603],{"className":1596},[635],[579,1598,1600],{"className":1599},[635,1023],[579,1601,981],{"className":1602},[635],[579,1604,1606],{"className":1605},[651],[579,1607,1609],{"className":1608},[655],[579,1610,1612],{"className":1611},[659],[579,1613,1615],{"className":1614,"style":1302},[663],[579,1616,1617,1620],{"style":1305},[579,1618],{"className":1619,"style":671},[670],[579,1621,1623],{"className":1622},[675,676,677,678],[579,1624,600],{"className":1625},[635,678],[563,1627,1628,1629,1694,1695,1760],{},"Für das Etikett einer Dose mit ",[579,1630,1632,1655],{"className":1631},[582],[579,1633,1635],{"className":1634},[586],[588,1636,1637],{"xmlns":590},[592,1638,1639,1652],{},[595,1640,1641,1643,1645,1648,1650],{},[602,1642,610],{},[705,1644,707],{},[598,1646,1647],{},"4",[976,1649,978],{},[976,1651,981],{},[614,1653,1654],{"encoding":616},"r = 4\\,\\text{cm}",[579,1656,1658,1676],{"className":1657,"ariaHidden":622},[621],[579,1659,1661,1664,1667,1670,1673],{"className":1660},[626],[579,1662],{"className":1663,"style":994},[630],[579,1665,610],{"className":1666,"style":647},[635,639],[579,1668],{"className":1669,"style":738},[737],[579,1671,707],{"className":1672},[742],[579,1674],{"className":1675,"style":738},[737],[579,1677,1679,1682,1685,1688],{"className":1678},[626],[579,1680],{"className":1681,"style":827},[630],[579,1683,1647],{"className":1684},[635],[579,1686],{"className":1687,"style":1019},[737],[579,1689,1691],{"className":1690},[635,1023],[579,1692,981],{"className":1693},[635]," und ",[579,1696,1698,1721],{"className":1697},[582],[579,1699,1701],{"className":1700},[586],[588,1702,1703],{"xmlns":590},[592,1704,1705,1718],{},[595,1706,1707,1709,1711,1714,1716],{},[602,1708,716],{},[705,1710,707],{},[598,1712,1713],{},"12",[976,1715,978],{},[976,1717,981],{},[614,1719,1720],{"encoding":616},"h = 12\\,\\text{cm}",[579,1722,1724,1742],{"className":1723,"ariaHidden":622},[621],[579,1725,1727,1730,1733,1736,1739],{"className":1726},[626],[579,1728],{"className":1729,"style":752},[630],[579,1731,716],{"className":1732},[635,639],[579,1734],{"className":1735,"style":738},[737],[579,1737,707],{"className":1738},[742],[579,1740],{"className":1741,"style":738},[737],[579,1743,1745,1748,1751,1754],{"className":1744},[626],[579,1746],{"className":1747,"style":827},[630],[579,1749,1713],{"className":1750},[635],[579,1752],{"className":1753,"style":1019},[737],[579,1755,1757],{"className":1756},[635,1023],[579,1758,981],{"className":1759},[635]," braucht man nur den Mantel:",[579,1762,1764],{"className":1763},[1097],[579,1765,1767,1831],{"className":1766},[582],[579,1768,1770],{"className":1769},[586],[588,1771,1772],{"xmlns":590,"display":1106},[592,1773,1774,1828],{},[595,1775,1776,1778,1780,1782,1784,1786,1788,1790,1792,1794,1796,1798,1800,1802,1805,1807,1809,1815,1817,1820,1822],{},[602,1777,703],{},[705,1779,707],{},[598,1781,600],{},[602,1783,604],{},[705,1785,1121],{},[598,1787,1647],{},[976,1789,978],{},[976,1791,981],{},[705,1793,1121],{},[598,1795,1713],{},[976,1797,978],{},[976,1799,981],{},[705,1801,707],{},[598,1803,1804],{},"96",[602,1806,604],{},[976,1808,978],{},[606,1810,1811,1813],{},[976,1812,981],{},[598,1814,600],{},[705,1816,1205],{},[598,1818,1819],{},"301,59",[976,1821,978],{},[606,1823,1824,1826],{},[976,1825,981],{},[598,1827,600],{},[614,1829,1830],{"encoding":616},"M = 2\\pi \\cdot 4\\,\\text{cm} \\cdot 12\\,\\text{cm} = 96\\pi\\,\\text{cm}^2 \\approx 301{,}59\\,\\text{cm}^2",[579,1832,1834,1852,1873,1900,1927,1983],{"className":1833,"ariaHidden":622},[621],[579,1835,1837,1840,1843,1846,1849],{"className":1836},[626],[579,1838],{"className":1839,"style":729},[630],[579,1841,703],{"className":1842,"style":733},[635,639],[579,1844],{"className":1845,"style":738},[737],[579,1847,707],{"className":1848},[742],[579,1850],{"className":1851,"style":738},[737],[579,1853,1855,1858,1861,1864,1867,1870],{"className":1854},[626],[579,1856],{"className":1857,"style":827},[630],[579,1859,600],{"className":1860},[635],[579,1862,604],{"className":1863,"style":640},[635,639],[579,1865],{"className":1866,"style":928},[737],[579,1868,1121],{"className":1869},[932],[579,1871],{"className":1872,"style":928},[737],[579,1874,1876,1879,1882,1885,1891,1894,1897],{"className":1875},[626],[579,1877],{"className":1878,"style":827},[630],[579,1880,1647],{"className":1881},[635],[579,1883],{"className":1884,"style":1019},[737],[579,1886,1888],{"className":1887},[635,1023],[579,1889,981],{"className":1890},[635],[579,1892],{"className":1893,"style":928},[737],[579,1895,1121],{"className":1896},[932],[579,1898],{"className":1899,"style":928},[737],[579,1901,1903,1906,1909,1912,1918,1921,1924],{"className":1902},[626],[579,1904],{"className":1905,"style":827},[630],[579,1907,1713],{"className":1908},[635],[579,1910],{"className":1911,"style":1019},[737],[579,1913,1915],{"className":1914},[635,1023],[579,1916,981],{"className":1917},[635],[579,1919],{"className":1920,"style":738},[737],[579,1922,707],{"className":1923},[742],[579,1925],{"className":1926,"style":738},[737],[579,1928,1930,1933,1936,1939,1942,1974,1977,1980],{"className":1929},[626],[579,1931],{"className":1932,"style":1302},[630],[579,1934,1804],{"className":1935},[635],[579,1937,604],{"className":1938,"style":640},[635,639],[579,1940],{"className":1941,"style":1019},[737],[579,1943,1945,1951],{"className":1944},[635],[579,1946,1948],{"className":1947},[635,1023],[579,1949,981],{"className":1950},[635],[579,1952,1954],{"className":1953},[651],[579,1955,1957],{"className":1956},[655],[579,1958,1960],{"className":1959},[659],[579,1961,1963],{"className":1962,"style":1302},[663],[579,1964,1965,1968],{"style":1305},[579,1966],{"className":1967,"style":671},[670],[579,1969,1971],{"className":1970},[675,676,677,678],[579,1972,600],{"className":1973},[635,678],[579,1975],{"className":1976,"style":738},[737],[579,1978,1205],{"className":1979},[742],[579,1981],{"className":1982,"style":738},[737],[579,1984,1986,1989,1993,1999,2003,2006],{"className":1985},[626],[579,1987],{"className":1988,"style":1574},[630],[579,1990,1992],{"className":1991},[635],"301",[579,1994,1996],{"className":1995},[635],[579,1997,1586],{"className":1998},[1585],[579,2000,2002],{"className":2001},[635],"59",[579,2004],{"className":2005,"style":1019},[737],[579,2007,2009,2015],{"className":2008},[635],[579,2010,2012],{"className":2011},[635,1023],[579,2013,981],{"className":2014},[635],[579,2016,2018],{"className":2017},[651],[579,2019,2021],{"className":2020},[655],[579,2022,2024],{"className":2023},[659],[579,2025,2027],{"className":2026,"style":1302},[663],[579,2028,2029,2032],{"style":1305},[579,2030],{"className":2031,"style":671},[670],[579,2033,2035],{"className":2034},[675,676,677,678],[579,2036,600],{"className":2037},[635,678],[558,2039,2041],{"id":2040},"typische-fehler","Typische Fehler",[572,2043,2044,2051,2141],{},[575,2045,2046,2047,2050],{},"Nur einen Kreis zählen. Ein geschlossener Zylinder hat Boden ",[567,2048,2049],{},"und"," Deckel.",[575,2052,2053,2054,2140],{},"Für den Mantel ",[579,2055,2057,2081],{"className":2056},[582],[579,2058,2060],{"className":2059},[586],[588,2061,2062],{"xmlns":590},[592,2063,2064,2078],{},[595,2065,2066,2068,2074,2076],{},[602,2067,604],{},[606,2069,2070,2072],{},[602,2071,610],{},[598,2073,600],{},[705,2075,1121],{},[602,2077,716],{},[614,2079,2080],{"encoding":616},"\\pi r^2 \\cdot h",[579,2082,2084,2131],{"className":2083,"ariaHidden":622},[621],[579,2085,2087,2090,2093,2122,2125,2128],{"className":2086},[626],[579,2088],{"className":2089,"style":631},[630],[579,2091,604],{"className":2092,"style":640},[635,639],[579,2094,2096,2099],{"className":2095},[635],[579,2097,610],{"className":2098,"style":647},[635,639],[579,2100,2102],{"className":2101},[651],[579,2103,2105],{"className":2104},[655],[579,2106,2108],{"className":2107},[659],[579,2109,2111],{"className":2110,"style":631},[663],[579,2112,2113,2116],{"style":666},[579,2114],{"className":2115,"style":671},[670],[579,2117,2119],{"className":2118},[675,676,677,678],[579,2120,600],{"className":2121},[635,678],[579,2123],{"className":2124,"style":928},[737],[579,2126,1121],{"className":2127},[932],[579,2129],{"className":2130,"style":928},[737],[579,2132,2134,2137],{"className":2133},[626],[579,2135],{"className":2136,"style":752},[630],[579,2138,716],{"className":2139},[635,639]," rechnen. Das ist das Volumen, nicht die Mantelfläche.",[575,2142,2143,2144,837],{},"Bei einem offenen Gefäß (z.B. Glas ohne Deckel) trotzdem beide Kreise zählen. Dann ist ",[579,2145,2147,2181],{"className":2146},[582],[579,2148,2150],{"className":2149},[586],[588,2151,2152],{"xmlns":590},[592,2153,2154,2178],{},[595,2155,2156,2158,2160,2162,2168,2170,2172,2174,2176],{},[602,2157,855],{},[705,2159,707],{},[602,2161,604],{},[606,2163,2164,2166],{},[602,2165,610],{},[598,2167,600],{},[705,2169,872],{},[598,2171,600],{},[602,2173,604],{},[602,2175,610],{},[602,2177,716],{},[614,2179,2180],{"encoding":616},"O = \\pi r^2 + 2\\pi r h",[579,2182,2184,2202,2250],{"className":2183,"ariaHidden":622},[621],[579,2185,2187,2190,2193,2196,2199],{"className":2186},[626],[579,2188],{"className":2189,"style":729},[630],[579,2191,855],{"className":2192,"style":647},[635,639],[579,2194],{"className":2195,"style":738},[737],[579,2197,707],{"className":2198},[742],[579,2200],{"className":2201,"style":738},[737],[579,2203,2205,2209,2212,2241,2244,2247],{"className":2204},[626],[579,2206],{"className":2207,"style":2208},[630],"height:0.8974em;vertical-align:-0.0833em;",[579,2210,604],{"className":2211,"style":640},[635,639],[579,2213,2215,2218],{"className":2214},[635],[579,2216,610],{"className":2217,"style":647},[635,639],[579,2219,2221],{"className":2220},[651],[579,2222,2224],{"className":2223},[655],[579,2225,2227],{"className":2226},[659],[579,2228,2230],{"className":2229,"style":631},[663],[579,2231,2232,2235],{"style":666},[579,2233],{"className":2234,"style":671},[670],[579,2236,2238],{"className":2237},[675,676,677,678],[579,2239,600],{"className":2240},[635,678],[579,2242],{"className":2243,"style":928},[737],[579,2245,872],{"className":2246},[932],[579,2248],{"className":2249,"style":928},[737],[579,2251,2253,2256,2259,2262,2265],{"className":2252},[626],[579,2254],{"className":2255,"style":752},[630],[579,2257,600],{"className":2258},[635],[579,2260,604],{"className":2261,"style":640},[635,639],[579,2263,610],{"className":2264,"style":647},[635,639],[579,2266,716],{"className":2267},[635,639],{"title":2269,"searchDepth":2270,"depth":2270,"links":2271},"",2,[2272,2273,2274],{"id":560,"depth":2270,"text":561},{"id":951,"depth":2270,"text":952},{"id":2040,"depth":2270,"text":2041},[2276,2279,2282,2285,2288],{"lhs":2277,"rhs":2278},"2*pi*r^2 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xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 206.4 194.4\" width=\"206.4\" height=\"194.4\" role=\"img\" aria-label=\"Zylinder mit Radius r und Höhe h: zwei Kreisflächen und der Mantel\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-cylinder-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-cylinder-surface-clip\">\u003Crect x=\"0\" y=\"0\" width=\"206.4\" height=\"194.4\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"24,158.4 25.1,162.14 28.32,165.79 33.65,169.2 40.85,172.27 49.73,174.96 60,177.12 71.38,178.7 83.52,179.66 96,180 108.48,179.66 120.62,178.7 132,177.12 142.27,174.96 151.15,172.27 158.35,169.2 163.68,165.79 166.9,162.14 168,158.4 168,33.6 166.9,29.86 163.68,26.21 158.35,22.8 151.15,19.73 142.27,17.04 132,14.88 120.62,13.3 108.48,12.34 96,12 83.52,12.34 71.38,13.3 60,14.88 49.73,17.04 40.85,19.73 33.65,22.8 28.32,26.21 25.1,29.86 24,33.6\" class=\"fig-muted fig-fill\"\u002F>\u003Cpath d=\"M 168 158.4 A 72 21.6 0 0 0 24 158.4\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 24 158.4 A 72 21.6 0 0 0 168 158.4\" class=\"fig-main\"\u002F>\u003Cline x1=\"24\" y1=\"158.4\" x2=\"24\" y2=\"33.6\" class=\"fig-main\"\u002F>\u003Cline x1=\"168\" y1=\"158.4\" x2=\"168\" y2=\"33.6\" class=\"fig-main\"\u002F>\u003Cellipse cx=\"96\" cy=\"33.6\" rx=\"72\" ry=\"21.6\" class=\"fig-main\"\u002F>\u003Cline x1=\"96\" y1=\"33.6\" x2=\"168\" y2=\"33.6\" class=\"fig-main\"\u002F>\u003Ccircle cx=\"96\" cy=\"33.6\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"132\" y=\"23.04\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">r\u003C\u002Ftext>\u003Ctext x=\"182.4\" y=\"96\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">h\u003C\u002Ftext>\u003C\u002Fsvg>","cylinder-surface","O = 2 \\pi r^2 + 2 \\pi r h","\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>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>π\u003C\u002Fmi>\u003Cmsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>π\u003C\u002Fmi>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">O = 2 \\pi r^2 + 2 \\pi r h\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\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\">2\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\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\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-zylinder",[],[2423,2424,2425],"cylinder-volume","circle-area","circle-circumference",{"title":548,"description":2269},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-zylinder","Die Oberfläche eines Zylinders besteht aus zwei Kreisen und dem Mantel, einem aufgerollten Rechteck.",[2430,2431,2432,2433,2434],"oberfläche","zylinder","mantelfläche","kreis","körper",[2436,2439,2442,2445],{"symbol":855,"meaning":2437,"symbolHtml":2438},"Oberflächeninhalt des Zylinders","\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":610,"meaning":2440,"symbolHtml":2441},"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":716,"meaning":2443,"symbolHtml":2444},"Höhe des Zylinders","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>h\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">h\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">h\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2446,"meaning":2447,"symbolHtml":2448},"\\pi","Kreiszahl, ungefähr 3,14159","\u003Cspan class=\"katex\">\u003Cspan 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