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r_i)",[575,1073,1075,1093,1158,1260],{"className":1074,"ariaHidden":644},[675],[575,1076,1078,1081,1084,1087,1090],{"className":1077},[679],[575,1079],{"className":1080,"style":684},[683],[575,1082,601],{"className":1083},[688,689],[575,1085],{"className":1086,"style":694},[693],[575,1088,605],{"className":1089},[698],[575,1091],{"className":1092,"style":694},[693],[575,1094,1096,1100,1103,1106,1149,1152,1155],{"className":1095},[679],[575,1097],{"className":1098,"style":1099},[683],"height:1em;vertical-align:-0.25em;",[575,1101,608],{"className":1102,"style":712},[688,689],[575,1104,645],{"className":1105},[883],[575,1107,1109,1112],{"className":1108},[688],[575,1110,614],{"className":1111,"style":719},[688,689],[575,1113,1115],{"className":1114},[723],[575,1116,1118,1140],{"className":1117},[727,728],[575,1119,1121,1137],{"className":1120},[732],[575,1122,1125],{"className":1123,"style":1124},[736],"height:0.1514em;",[575,1126,1128,1131],{"style":1127},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[575,1129],{"className":1130,"style":745},[744],[575,1132,1134],{"className":1133},[749,750,751,752],[575,1135,617],{"className":1136},[688,689,752],[575,1138,772],{"className":1139},[771],[575,1141,1143],{"className":1142},[732],[575,1144,1147],{"className":1145,"style":1146},[736],"height:0.15em;",[575,1148],{},[575,1150],{"className":1151,"style":785},[693],[575,1153,1042],{"className":1154},[789],[575,1156],{"className":1157,"style":785},[693],[575,1159,1161,1164,1205,1208,1211,1251,1254,1257],{"className":1160},[679],[575,1162],{"className":1163,"style":1099},[683],[575,1165,1167,1170],{"className":1166},[688],[575,1168,614],{"className":1169,"style":719},[688,689],[575,1171,1173],{"className":1172},[723],[575,1174,1176,1197],{"className":1175},[727,728],[575,1177,1179,1194],{"className":1178},[732],[575,1180,1183],{"className":1181,"style":1182},[736],"height:0.3117em;",[575,1184,1185,1188],{"style":1127},[575,1186],{"className":1187,"style":745},[744],[575,1189,1191],{"className":1190},[749,750,751,752],[575,1192,633],{"className":1193},[688,689,752],[575,1195,772],{"className":1196},[771],[575,1198,1200],{"className":1199},[732],[575,1201,1203],{"className":1202,"style":1146},[736],[575,1204],{},[575,1206,666],{"className":1207},[1005],[575,1209,645],{"className":1210},[883],[575,1212,1214,1217],{"className":1213},[688],[575,1215,614],{"className":1216,"style":719},[688,689],[575,1218,1220],{"className":1219},[723],[575,1221,1223,1243],{"className":1222},[727,728],[575,1224,1226,1240],{"className":1225},[732],[575,1227,1229],{"className":1228,"style":1124},[736],[575,1230,1231,1234],{"style":1127},[575,1232],{"className":1233,"style":745},[744],[575,1235,1237],{"className":1236},[749,750,751,752],[575,1238,617],{"className":1239},[688,689,752],[575,1241,772],{"className":1242},[771],[575,1244,1246],{"className":1245},[732],[575,1247,1249],{"className":1248,"style":1146},[736],[575,1250],{},[575,1252],{"className":1253,"style":785},[693],[575,1255,624],{"className":1256},[789],[575,1258],{"className":1259,"style":785},[693],[575,1261,1263,1266,1306],{"className":1262},[679],[575,1264],{"className":1265,"style":1099},[683],[575,1267,1269,1272],{"className":1268},[688],[575,1270,614],{"className":1271,"style":719},[688,689],[575,1273,1275],{"className":1274},[723],[575,1276,1278,1298],{"className":1277},[727,728],[575,1279,1281,1295],{"className":1280},[732],[575,1282,1284],{"className":1283,"style":1182},[736],[575,1285,1286,1289],{"style":1127},[575,1287],{"className":1288,"style":745},[744],[575,1290,1292],{"className":1291},[749,750,751,752],[575,1293,633],{"className":1294},[688,689,752],[575,1296,772],{"className":1297},[771],[575,1299,1301],{"className":1300},[732],[575,1302,1304],{"className":1303,"style":1146},[736],[575,1305],{},[575,1307,666],{"className":1308},[1005]," schreiben.",[559,1311,1313],{"id":1312},"beispiele","Beispiele",[564,1315,1316,1317,1365,1366,1409],{},"Ein Kreisring hat den Außenradius ",[575,1318,1320,1342],{"className":1319},[582],[575,1321,1323],{"className":1322},[586],[588,1324,1325],{"xmlns":590},[593,1326,1327,1339],{},[596,1328,1329,1332,1336],{},[619,1330,1331],{},"5",[1333,1334,1335],"mtext",{}," ",[1333,1337,1338],{},"cm",[668,1340,1341],{"encoding":670},"5\\,\\text{cm}",[575,1343,1345],{"className":1344,"ariaHidden":644},[675],[575,1346,1348,1352,1355,1358],{"className":1347},[679],[575,1349],{"className":1350,"style":1351},[683],"height:0.6444em;",[575,1353,1331],{"className":1354},[688],[575,1356],{"className":1357,"style":875},[693],[575,1359,1362],{"className":1360},[688,1361],"text",[575,1363,1338],{"className":1364},[688]," und den Innenradius ",[575,1367,1369,1388],{"className":1368},[582],[575,1370,1372],{"className":1371},[586],[588,1373,1374],{"xmlns":590},[593,1375,1376,1385],{},[596,1377,1378,1381,1383],{},[619,1379,1380],{},"3",[1333,1382,1335],{},[1333,1384,1338],{},[668,1386,1387],{"encoding":670},"3\\,\\text{cm}",[575,1389,1391],{"className":1390,"ariaHidden":644},[675],[575,1392,1394,1397,1400,1403],{"className":1393},[679],[575,1395],{"className":1396,"style":1351},[683],[575,1398,1380],{"className":1399},[688],[575,1401],{"className":1402,"style":875},[693],[575,1404,1406],{"className":1405},[688,1361],[575,1407,1338],{"className":1408},[688],":",[575,1411,1413],{"className":1412},[578],[575,1414,1416,1492],{"className":1415},[582],[575,1417,1419],{"className":1418},[586],[588,1420,1421],{"xmlns":590,"display":591},[593,1422,1423,1489],{},[596,1424,1425,1427,1429,1431,1452,1454,1460,1462,1465,1467,1469,1475,1478,1481,1483],{},[599,1426,601],{},[603,1428,605],{},[599,1430,608],{},[596,1432,1433,1435,1442,1444,1450],{},[603,1434,645],{"fence":644},[1436,1437,1438,1440],"msup",{},[619,1439,1331],{},[619,1441,621],{},[603,1443,624],{},[1436,1445,1446,1448],{},[619,1447,1380],{},[619,1449,621],{},[603,1451,666],{"fence":644},[1333,1453,1335],{},[1436,1455,1456,1458],{},[1333,1457,1338],{},[619,1459,621],{},[603,1461,605],{},[619,1463,1464],{},"16",[599,1466,608],{},[1333,1468,1335],{},[1436,1470,1471,1473],{},[1333,1472,1338],{},[619,1474,621],{},[603,1476,1477],{},"≈",[619,1479,1480],{},"50,27",[1333,1482,1335],{},[1436,1484,1485,1487],{},[1333,1486,1338],{},[619,1488,621],{},[668,1490,1491],{"encoding":670},"A = \\pi \\left(5^2 - 3^2\\right)\\,\\text{cm}^2 = 16\\pi\\,\\text{cm}^2 \\approx 50{,}27\\,\\text{cm}^2",[575,1493,1495,1513,1654,1710],{"className":1494,"ariaHidden":644},[675],[575,1496,1498,1501,1504,1507,1510],{"className":1497},[679],[575,1499],{"className":1500,"style":684},[683],[575,1502,601],{"className":1503},[688,689],[575,1505],{"className":1506,"style":694},[693],[575,1508,605],{"className":1509},[698],[575,1511],{"className":1512,"style":694},[693],[575,1514,1516,1519,1522,1525,1607,1610,1613,1645,1648,1651],{"className":1515},[679],[575,1517],{"className":1518,"style":868},[683],[575,1520,608],{"className":1521,"style":712},[688,689],[575,1523],{"className":1524,"style":875},[693],[575,1526,1528,1534,1563,1566,1569,1572,1601],{"className":1527},[879],[575,1529,1531],{"className":1530,"style":885},[883,884],[575,1532,645],{"className":1533},[889,890],[575,1535,1537,1540],{"className":1536},[688],[575,1538,1331],{"className":1539},[688],[575,1541,1543],{"className":1542},[723],[575,1544,1546],{"className":1545},[727],[575,1547,1549],{"className":1548},[732],[575,1550,1552],{"className":1551,"style":737},[736],[575,1553,1554,1557],{"style":758},[575,1555],{"className":1556,"style":745},[744],[575,1558,1560],{"className":1559},[749,750,751,752],[575,1561,621],{"className":1562},[688,752],[575,1564],{"className":1565,"style":785},[693],[575,1567,624],{"className":1568},[789],[575,1570],{"className":1571,"style":785},[693],[575,1573,1575,1578],{"className":1574},[688],[575,1576,1380],{"className":1577},[688],[575,1579,1581],{"className":1580},[723],[575,1582,1584],{"className":1583},[727],[575,1585,1587],{"className":1586},[732],[575,1588,1590],{"className":1589,"style":737},[736],[575,1591,1592,1595],{"style":758},[575,1593],{"className":1594,"style":745},[744],[575,1596,1598],{"className":1597},[749,750,751,752],[575,1599,621],{"className":1600},[688,752],[575,1602,1604],{"className":1603,"style":885},[1005,884],[575,1605,666],{"className":1606},[889,890],[575,1608],{"className":1609,"style":875},[693],[575,1611],{"className":1612,"style":875},[693],[575,1614,1616,1622],{"className":1615},[688],[575,1617,1619],{"className":1618},[688,1361],[575,1620,1338],{"className":1621},[688],[575,1623,1625],{"className":1624},[723],[575,1626,1628],{"className":1627},[727],[575,1629,1631],{"className":1630},[732],[575,1632,1634],{"className":1633,"style":737},[736],[575,1635,1636,1639],{"style":758},[575,1637],{"className":1638,"style":745},[744],[575,1640,1642],{"className":1641},[749,750,751,752],[575,1643,621],{"className":1644},[688,752],[575,1646],{"className":1647,"style":694},[693],[575,1649,605],{"className":1650},[698],[575,1652],{"className":1653,"style":694},[693],[575,1655,1657,1660,1663,1666,1669,1701,1704,1707],{"className":1656},[679],[575,1658],{"className":1659,"style":737},[683],[575,1661,1464],{"className":1662},[688],[575,1664,608],{"className":1665,"style":712},[688,689],[575,1667],{"className":1668,"style":875},[693],[575,1670,1672,1678],{"className":1671},[688],[575,1673,1675],{"className":1674},[688,1361],[575,1676,1338],{"className":1677},[688],[575,1679,1681],{"className":1680},[723],[575,1682,1684],{"className":1683},[727],[575,1685,1687],{"className":1686},[732],[575,1688,1690],{"className":1689,"style":737},[736],[575,1691,1692,1695],{"style":758},[575,1693],{"className":1694,"style":745},[744],[575,1696,1698],{"className":1697},[749,750,751,752],[575,1699,621],{"className":1700},[688,752],[575,1702],{"className":1703,"style":694},[693],[575,1705,1477],{"className":1706},[698],[575,1708],{"className":1709,"style":694},[693],[575,1711,1713,1717,1721,1729,1733,1736],{"className":1712},[679],[575,1714],{"className":1715,"style":1716},[683],"height:1.0585em;vertical-align:-0.1944em;",[575,1718,1720],{"className":1719},[688],"50",[575,1722,1724],{"className":1723},[688],[575,1725,1728],{"className":1726},[1727],"mpunct",",",[575,1730,1732],{"className":1731},[688],"27",[575,1734],{"className":1735,"style":875},[693],[575,1737,1739,1745],{"className":1738},[688],[575,1740,1742],{"className":1741},[688,1361],[575,1743,1338],{"className":1744},[688],[575,1746,1748],{"className":1747},[723],[575,1749,1751],{"className":1750},[727],[575,1752,1754],{"className":1753},[732],[575,1755,1757],{"className":1756,"style":737},[736],[575,1758,1759,1762],{"style":758},[575,1760],{"className":1761,"style":745},[744],[575,1763,1765],{"className":1764},[749,750,751,752],[575,1766,621],{"className":1767},[688,752],[564,1769,1770,1771,1814,1815,1858,1859,1966,1967,2072],{},"Eine CD hat einen Durchmesser von ",[575,1772,1774,1793],{"className":1773},[582],[575,1775,1777],{"className":1776},[586],[588,1778,1779],{"xmlns":590},[593,1780,1781,1790],{},[596,1782,1783,1786,1788],{},[619,1784,1785],{},"12",[1333,1787,1335],{},[1333,1789,1338],{},[668,1791,1792],{"encoding":670},"12\\,\\text{cm}",[575,1794,1796],{"className":1795,"ariaHidden":644},[675],[575,1797,1799,1802,1805,1808],{"className":1798},[679],[575,1800],{"className":1801,"style":1351},[683],[575,1803,1785],{"className":1804},[688],[575,1806],{"className":1807,"style":875},[693],[575,1809,1811],{"className":1810},[688,1361],[575,1812,1338],{"className":1813},[688],", das Loch in der Mitte einen Durchmesser von ",[575,1816,1818,1837],{"className":1817},[582],[575,1819,1821],{"className":1820},[586],[588,1822,1823],{"xmlns":590},[593,1824,1825,1834],{},[596,1826,1827,1830,1832],{},[619,1828,1829],{},"4",[1333,1831,1335],{},[1333,1833,1338],{},[668,1835,1836],{"encoding":670},"4\\,\\text{cm}",[575,1838,1840],{"className":1839,"ariaHidden":644},[675],[575,1841,1843,1846,1849,1852],{"className":1842},[679],[575,1844],{"className":1845,"style":1351},[683],[575,1847,1829],{"className":1848},[688],[575,1850],{"className":1851,"style":875},[693],[575,1853,1855],{"className":1854},[688,1361],[575,1856,1338],{"className":1857},[688],". Zuerst die Radien bestimmen: ",[575,1860,1862,1889],{"className":1861},[582],[575,1863,1865],{"className":1864},[586],[588,1866,1867],{"xmlns":590},[593,1868,1869,1886],{},[596,1870,1871,1877,1879,1882,1884],{},[1034,1872,1873,1875],{},[599,1874,614],{},[599,1876,617],{},[603,1878,605],{},[619,1880,1881],{},"6",[1333,1883,1335],{},[1333,1885,1338],{},[668,1887,1888],{"encoding":670},"r_a = 6\\,\\text{cm}",[575,1890,1892,1948],{"className":1891,"ariaHidden":644},[675],[575,1893,1895,1899,1939,1942,1945],{"className":1894},[679],[575,1896],{"className":1897,"style":1898},[683],"height:0.5806em;vertical-align:-0.15em;",[575,1900,1902,1905],{"className":1901},[688],[575,1903,614],{"className":1904,"style":719},[688,689],[575,1906,1908],{"className":1907},[723],[575,1909,1911,1931],{"className":1910},[727,728],[575,1912,1914,1928],{"className":1913},[732],[575,1915,1917],{"className":1916,"style":1124},[736],[575,1918,1919,1922],{"style":1127},[575,1920],{"className":1921,"style":745},[744],[575,1923,1925],{"className":1924},[749,750,751,752],[575,1926,617],{"className":1927},[688,689,752],[575,1929,772],{"className":1930},[771],[575,1932,1934],{"className":1933},[732],[575,1935,1937],{"className":1936,"style":1146},[736],[575,1938],{},[575,1940],{"className":1941,"style":694},[693],[575,1943,605],{"className":1944},[698],[575,1946],{"className":1947,"style":694},[693],[575,1949,1951,1954,1957,1960],{"className":1950},[679],[575,1952],{"className":1953,"style":1351},[683],[575,1955,1881],{"className":1956},[688],[575,1958],{"className":1959,"style":875},[693],[575,1961,1963],{"className":1962},[688,1361],[575,1964,1338],{"className":1965},[688]," und ",[575,1968,1970,1996],{"className":1969},[582],[575,1971,1973],{"className":1972},[586],[588,1974,1975],{"xmlns":590},[593,1976,1977,1993],{},[596,1978,1979,1985,1987,1989,1991],{},[1034,1980,1981,1983],{},[599,1982,614],{},[599,1984,633],{},[603,1986,605],{},[619,1988,621],{},[1333,1990,1335],{},[1333,1992,1338],{},[668,1994,1995],{"encoding":670},"r_i = 2\\,\\text{cm}",[575,1997,1999,2054],{"className":1998,"ariaHidden":644},[675],[575,2000,2002,2005,2045,2048,2051],{"className":2001},[679],[575,2003],{"className":2004,"style":1898},[683],[575,2006,2008,2011],{"className":2007},[688],[575,2009,614],{"className":2010,"style":719},[688,689],[575,2012,2014],{"className":2013},[723],[575,2015,2017,2037],{"className":2016},[727,728],[575,2018,2020,2034],{"className":2019},[732],[575,2021,2023],{"className":2022,"style":1182},[736],[575,2024,2025,2028],{"style":1127},[575,2026],{"className":2027,"style":745},[744],[575,2029,2031],{"className":2030},[749,750,751,752],[575,2032,633],{"className":2033},[688,689,752],[575,2035,772],{"className":2036},[771],[575,2038,2040],{"className":2039},[732],[575,2041,2043],{"className":2042,"style":1146},[736],[575,2044],{},[575,2046],{"className":2047,"style":694},[693],[575,2049,605],{"className":2050},[698],[575,2052],{"className":2053,"style":694},[693],[575,2055,2057,2060,2063,2066],{"className":2056},[679],[575,2058],{"className":2059,"style":1351},[683],[575,2061,621],{"className":2062},[688],[575,2064],{"className":2065,"style":875},[693],[575,2067,2069],{"className":2068},[688,1361],[575,2070,1338],{"className":2071},[688],".",[575,2074,2076],{"className":2075},[578],[575,2077,2079,2153],{"className":2078},[582],[575,2080,2082],{"className":2081},[586],[588,2083,2084],{"xmlns":590,"display":591},[593,2085,2086,2150],{},[596,2087,2088,2090,2092,2094,2114,2116,2122,2124,2127,2129,2131,2137,2139,2142,2144],{},[599,2089,601],{},[603,2091,605],{},[599,2093,608],{},[596,2095,2096,2098,2104,2106,2112],{},[603,2097,645],{"fence":644},[1436,2099,2100,2102],{},[619,2101,1881],{},[619,2103,621],{},[603,2105,624],{},[1436,2107,2108,2110],{},[619,2109,621],{},[619,2111,621],{},[603,2113,666],{"fence":644},[1333,2115,1335],{},[1436,2117,2118,2120],{},[1333,2119,1338],{},[619,2121,621],{},[603,2123,605],{},[619,2125,2126],{},"32",[599,2128,608],{},[1333,2130,1335],{},[1436,2132,2133,2135],{},[1333,2134,1338],{},[619,2136,621],{},[603,2138,1477],{},[619,2140,2141],{},"100,53",[1333,2143,1335],{},[1436,2145,2146,2148],{},[1333,2147,1338],{},[619,2149,621],{},[668,2151,2152],{"encoding":670},"A = \\pi \\left(6^2 - 2^2\\right)\\,\\text{cm}^2 = 32\\pi\\,\\text{cm}^2 \\approx 100{,}53\\,\\text{cm}^2",[575,2154,2156,2174,2315,2371],{"className":2155,"ariaHidden":644},[675],[575,2157,2159,2162,2165,2168,2171],{"className":2158},[679],[575,2160],{"className":2161,"style":684},[683],[575,2163,601],{"className":2164},[688,689],[575,2166],{"className":2167,"style":694},[693],[575,2169,605],{"className":2170},[698],[575,2172],{"className":2173,"style":694},[693],[575,2175,2177,2180,2183,2186,2268,2271,2274,2306,2309,2312],{"className":2176},[679],[575,2178],{"className":2179,"style":868},[683],[575,2181,608],{"className":2182,"style":712},[688,689],[575,2184],{"className":2185,"style":875},[693],[575,2187,2189,2195,2224,2227,2230,2233,2262],{"className":2188},[879],[575,2190,2192],{"className":2191,"style":885},[883,884],[575,2193,645],{"className":2194},[889,890],[575,2196,2198,2201],{"className":2197},[688],[575,2199,1881],{"className":2200},[688],[575,2202,2204],{"className":2203},[723],[575,2205,2207],{"className":2206},[727],[575,2208,2210],{"className":2209},[732],[575,2211,2213],{"className":2212,"style":737},[736],[575,2214,2215,2218],{"style":758},[575,2216],{"className":2217,"style":745},[744],[575,2219,2221],{"className":2220},[749,750,751,752],[575,2222,621],{"className":2223},[688,752],[575,2225],{"className":2226,"style":785},[693],[575,2228,624],{"className":2229},[789],[575,2231],{"className":2232,"style":785},[693],[575,2234,2236,2239],{"className":2235},[688],[575,2237,621],{"className":2238},[688],[575,2240,2242],{"className":2241},[723],[575,2243,2245],{"className":2244},[727],[575,2246,2248],{"className":2247},[732],[575,2249,2251],{"className":2250,"style":737},[736],[575,2252,2253,2256],{"style":758},[575,2254],{"className":2255,"style":745},[744],[575,2257,2259],{"className":2258},[749,750,751,752],[575,2260,621],{"className":2261},[688,752],[575,2263,2265],{"className":2264,"style":885},[1005,884],[575,2266,666],{"className":2267},[889,890],[575,2269],{"className":2270,"style":875},[693],[575,2272],{"className":2273,"style":875},[693],[575,2275,2277,2283],{"className":2276},[688],[575,2278,2280],{"className":2279},[688,1361],[575,2281,1338],{"className":2282},[688],[575,2284,2286],{"className":2285},[723],[575,2287,2289],{"className":2288},[727],[575,2290,2292],{"className":2291},[732],[575,2293,2295],{"className":2294,"style":737},[736],[575,2296,2297,2300],{"style":758},[575,2298],{"className":2299,"style":745},[744],[575,2301,2303],{"className":2302},[749,750,751,752],[575,2304,621],{"className":2305},[688,752],[575,2307],{"className":2308,"style":694},[693],[575,2310,605],{"className":2311},[698],[575,2313],{"className":2314,"style":694},[693],[575,2316,2318,2321,2324,2327,2330,2362,2365,2368],{"className":2317},[679],[575,2319],{"className":2320,"style":737},[683],[575,2322,2126],{"className":2323},[688],[575,2325,608],{"className":2326,"style":712},[688,689],[575,2328],{"className":2329,"style":875},[693],[575,2331,2333,2339],{"className":2332},[688],[575,2334,2336],{"className":2335},[688,1361],[575,2337,1338],{"className":2338},[688],[575,2340,2342],{"className":2341},[723],[575,2343,2345],{"className":2344},[727],[575,2346,2348],{"className":2347},[732],[575,2349,2351],{"className":2350,"style":737},[736],[575,2352,2353,2356],{"style":758},[575,2354],{"className":2355,"style":745},[744],[575,2357,2359],{"className":2358},[749,750,751,752],[575,2360,621],{"className":2361},[688,752],[575,2363],{"className":2364,"style":694},[693],[575,2366,1477],{"className":2367},[698],[575,2369],{"className":2370,"style":694},[693],[575,2372,2374,2377,2381,2387,2391,2394],{"className":2373},[679],[575,2375],{"className":2376,"style":1716},[683],[575,2378,2380],{"className":2379},[688],"100",[575,2382,2384],{"className":2383},[688],[575,2385,1728],{"className":2386},[1727],[575,2388,2390],{"className":2389},[688],"53",[575,2392],{"className":2393,"style":875},[693],[575,2395,2397,2403],{"className":2396},[688],[575,2398,2400],{"className":2399},[688,1361],[575,2401,1338],{"className":2402},[688],[575,2404,2406],{"className":2405},[723],[575,2407,2409],{"className":2408},[727],[575,2410,2412],{"className":2411},[732],[575,2413,2415],{"className":2414,"style":737},[736],[575,2416,2417,2420],{"style":758},[575,2418],{"className":2419,"style":745},[744],[575,2421,2423],{"className":2422},[749,750,751,752],[575,2424,621],{"className":2425},[688,752],[559,2427,2429],{"id":2428},"typische-fehler","Typische Fehler",[2431,2432,2433,2901,2904],"ul",{},[2434,2435,2436,2437,2831,2832,2866,2867,2072],"li",{},"Erst die Radien subtrahieren und dann quadrieren: ",[575,2438,2440,2504],{"className":2439},[582],[575,2441,2443],{"className":2442},[586],[588,2444,2445],{"xmlns":590},[593,2446,2447,2501],{},[596,2448,2449,2451,2453,2459,2461,2467,2473,2477,2479,2481,2489,2491,2499],{},[599,2450,608],{},[603,2452,645],{"stretchy":1032},[1034,2454,2455,2457],{},[599,2456,614],{},[599,2458,617],{},[603,2460,624],{},[1034,2462,2463,2465],{},[599,2464,614],{},[599,2466,633],{},[1436,2468,2469,2471],{},[603,2470,666],{"stretchy":1032},[619,2472,621],{},[603,2474,2476],{"mathvariant":2475},"normal","≠",[599,2478,608],{},[603,2480,645],{"stretchy":1032},[610,2482,2483,2485,2487],{},[599,2484,614],{},[599,2486,617],{},[619,2488,621],{},[603,2490,624],{},[610,2492,2493,2495,2497],{},[599,2494,614],{},[599,2496,633],{},[619,2498,621],{},[603,2500,666],{"stretchy":1032},[668,2502,2503],{"encoding":670},"\\pi (r_a - r_i)^2 \\neq \\pi (r_a^2 - r_i^2)",[575,2505,2507,2568,2696,2768],{"className":2506,"ariaHidden":644},[675],[575,2508,2510,2513,2516,2519,2559,2562,2565],{"className":2509},[679],[575,2511],{"className":2512,"style":1099},[683],[575,2514,608],{"className":2515,"style":712},[688,689],[575,2517,645],{"className":2518},[883],[575,2520,2522,2525],{"className":2521},[688],[575,2523,614],{"className":2524,"style":719},[688,689],[575,2526,2528],{"className":2527},[723],[575,2529,2531,2551],{"className":2530},[727,728],[575,2532,2534,2548],{"className":2533},[732],[575,2535,2537],{"className":2536,"style":1124},[736],[575,2538,2539,2542],{"style":1127},[575,2540],{"className":2541,"style":745},[744],[575,2543,2545],{"className":2544},[749,750,751,752],[575,2546,617],{"className":2547},[688,689,752],[575,2549,772],{"className":2550},[771],[575,2552,2554],{"className":2553},[732],[575,2555,2557],{"className":2556,"style":1146},[736],[575,2558],{},[575,2560],{"className":2561,"style":785},[693],[575,2563,624],{"className":2564},[789],[575,2566],{"className":2567,"style":785},[693],[575,2569,2571,2575,2615,2646,2649,2693],{"className":2570},[679],[575,2572],{"className":2573,"style":2574},[683],"height:1.0641em;vertical-align:-0.25em;",[575,2576,2578,2581],{"className":2577},[688],[575,2579,614],{"className":2580,"style":719},[688,689],[575,2582,2584],{"className":2583},[723],[575,2585,2587,2607],{"className":2586},[727,728],[575,2588,2590,2604],{"className":2589},[732],[575,2591,2593],{"className":2592,"style":1182},[736],[575,2594,2595,2598],{"style":1127},[575,2596],{"className":2597,"style":745},[744],[575,2599,2601],{"className":2600},[749,750,751,752],[575,2602,633],{"className":2603},[688,689,752],[575,2605,772],{"className":2606},[771],[575,2608,2610],{"className":2609},[732],[575,2611,2613],{"className":2612,"style":1146},[736],[575,2614],{},[575,2616,2618,2621],{"className":2617},[1005],[575,2619,666],{"className":2620},[1005],[575,2622,2624],{"className":2623},[723],[575,2625,2627],{"className":2626},[727],[575,2628,2630],{"className":2629},[732],[575,2631,2634],{"className":2632,"style":2633},[736],"height:0.8141em;",[575,2635,2637,2640],{"style":2636},"top:-3.063em;margin-right:0.05em;",[575,2638],{"className":2639,"style":745},[744],[575,2641,2643],{"className":2642},[749,750,751,752],[575,2644,621],{"className":2645},[688,752],[575,2647],{"className":2648,"style":694},[693],[575,2650,2652,2686,2690],{"className":2651},[698],[575,2653,2655],{"className":2654},[698],[575,2656,2659],{"className":2657},[688,2658],"vbox",[575,2660,2663],{"className":2661},[2662],"thinbox",[575,2664,2667,2671,2682],{"className":2665},[2666],"rlap",[575,2668],{"className":2669,"style":2670},[683],"height:0.8889em;vertical-align:-0.1944em;",[575,2672,2675],{"className":2673},[2674],"inner",[575,2676,2678],{"className":2677},[688],[575,2679,2681],{"className":2680},[698],"",[575,2683],{"className":2684},[2685],"fix",[575,2687],{"className":2688},[693,2689],"nobreak",[575,2691,605],{"className":2692},[698],[575,2694],{"className":2695,"style":694},[693],[575,2697,2699,2702,2705,2708,2759,2762,2765],{"className":2698},[679],[575,2700],{"className":2701,"style":2574},[683],[575,2703,608],{"className":2704,"style":712},[688,689],[575,2706,645],{"className":2707},[883],[575,2709,2711,2714],{"className":2710},[688],[575,2712,614],{"className":2713,"style":719},[688,689],[575,2715,2717],{"className":2716},[723],[575,2718,2720,2751],{"className":2719},[727,728],[575,2721,2723,2748],{"className":2722},[732],[575,2724,2726,2737],{"className":2725,"style":2633},[736],[575,2727,2728,2731],{"style":740},[575,2729],{"className":2730,"style":745},[744],[575,2732,2734],{"className":2733},[749,750,751,752],[575,2735,617],{"className":2736},[688,689,752],[575,2738,2739,2742],{"style":2636},[575,2740],{"className":2741,"style":745},[744],[575,2743,2745],{"className":2744},[749,750,751,752],[575,2746,621],{"className":2747},[688,752],[575,2749,772],{"className":2750},[771],[575,2752,2754],{"className":2753},[732],[575,2755,2757],{"className":2756,"style":779},[736],[575,2758],{},[575,2760],{"className":2761,"style":785},[693],[575,2763,624],{"className":2764},[789],[575,2766],{"className":2767,"style":785},[693],[575,2769,2771,2775,2828],{"className":2770},[679],[575,2772],{"className":2773,"style":2774},[683],"height:1.0728em;vertical-align:-0.2587em;",[575,2776,2778,2781],{"className":2777},[688],[575,2779,614],{"className":2780,"style":719},[688,689],[575,2782,2784],{"className":2783},[723],[575,2785,2787,2819],{"className":2786},[727,728],[575,2788,2790,2816],{"className":2789},[732],[575,2791,2793,2805],{"className":2792,"style":2633},[736],[575,2794,2796,2799],{"style":2795},"top:-2.4413em;margin-left:-0.0278em;margin-right:0.05em;",[575,2797],{"className":2798,"style":745},[744],[575,2800,2802],{"className":2801},[749,750,751,752],[575,2803,633],{"className":2804},[688,689,752],[575,2806,2807,2810],{"style":2636},[575,2808],{"className":2809,"style":745},[744],[575,28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Im ersten Beispiel ergäbe das ",[575,2833,2835,2851],{"className":2834},[582],[575,2836,2838],{"className":2837},[586],[588,2839,2840],{"xmlns":590},[593,2841,2842,2848],{},[596,2843,2844,2846],{},[619,2845,1829],{},[599,2847,608],{},[668,2849,2850],{"encoding":670},"4\\pi",[575,2852,2854],{"className":2853,"ariaHidden":644},[675],[575,2855,2857,2860,2863],{"className":2856},[679],[575,2858],{"className":2859,"style":1351},[683],[575,2861,1829],{"className":2862},[688],[575,2864,608],{"className":2865,"style":712},[688,689]," statt ",[575,2868,2870,2886],{"className":2869},[582],[575,2871,2873],{"className":2872},[586],[588,2874,2875],{"xmlns":590},[593,2876,2877,2883],{},[596,2878,2879,2881],{},[619,2880,1464],{},[599,2882,608],{},[668,2884,2885],{"encoding":670},"16\\pi",[575,2887,2889],{"className":2888,"ariaHidden":644},[675],[575,2890,2892,2895,2898],{"className":2891},[679],[575,2893],{"className":2894,"style":1351},[683],[575,2896,1464],{"className":2897},[688],[575,2899,608],{"className":2900,"style":712},[688,689],[2434,2902,2903],{},"Durchmesser statt Radien einsetzen. Das liefert das Vierfache der richtigen Fläche.",[2434,2905,2906,2907,3072,3073,3156,3157,2072],{},"Die Klammer vergessen: ",[575,2908,2910,2942],{"className":2909},[582],[575,2911,2913],{"className":2912},[586],[588,2914,2915],{"xmlns":590},[593,2916,2917,2939],{},[596,2918,2919,2921,2929,2931],{},[599,2920,608],{},[610,2922,2923,2925,2927],{},[599,2924,614],{},[599,2926,617],{},[619,2928,621],{},[603,2930,624],{},[610,2932,2933,2935,2937],{},[599,2934,614],{},[599,2936,633],{},[619,2938,621],{},[668,2940,2941],{"encoding":670},"\\pi r_a^2 - r_i^2",[575,2943,2945,3015],{"className":2944,"ariaHidden":644},[675],[575,2946,2948,2952,2955,3006,3009,3012],{"className":2947},[679],[575,2949],{"className":2950,"style":2951},[683],"height:1.0611em;vertical-align:-0.247em;",[575,2953,608],{"className":2954,"style":712},[688,689],[575,2956,2958,2961],{"className":2957},[688],[575,2959,614],{"className":2960,"style":719},[688,689],[575,2962,2964],{"className":2963},[723],[575,2965,2967,2998],{"className":2966},[727,728],[575,2968,2970,2995],{"className":2969},[732],[575,2971,2973,2984],{"className":2972,"style":2633},[736],[575,2974,2975,2978],{"style":740},[575,2976],{"className":2977,"style":745},[744],[575,2979,2981],{"className":2980},[749,750,751,752],[575,2982,617],{"className":2983},[688,689,752],[575,2985,2986,2989],{"style":2636},[575,2987],{"className":2988,"style":745},[744],[575,2990,2992],{"className":2991},[749,750,751,752],[575,2993,621],{"className":2994},[688,752],[575,2996,772],{"className":2997},[771],[575,2999,3001],{"className":3000},[732],[575,3002,3004],{"className":3003,"style":779},[736],[575,3005],{},[575,3007],{"className":3008,"style":785},[693],[575,3010,624],{"className":3011},[789],[575,3013],{"className":3014,"style":785},[693],[575,3016,3018,3021],{"className":3017},[679],[575,3019],{"className":3020,"style":2774},[683],[575,3022,3024,3027],{"className":3023},[688],[575,3025,614],{"className":3026,"style":719},[688,689],[575,3028,3030],{"className":3029},[723],[575,3031,3033,3064],{"className":3032},[727,728],[575,3034,3036,3061],{"className":3035},[732],[575,3037,3039,3050],{"className":3038,"style":2633},[736],[575,3040,3041,3044],{"style":2795},[575,3042],{"className":3043,"style":745},[744],[575,3045,3047],{"className":3046},[749,750,751,752],[575,3048,633],{"className":3049},[688,689,752],[575,3051,3052,3055],{"style":2636},[575,3053],{"className":3054,"style":745},[744],[575,3056,3058],{"className":3057},[749,750,751,752],[575,3059,621],{"className":3060},[688,752],[575,3062,772],{"className":3063},[771],[575,3065,3067],{"className":3066},[732],[575,3068,3070],{"className":3069,"style":2825},[736],[575,3071],{}," zieht nur ",[575,3074,3076,3096],{"className":3075},[582],[575,3077,3079],{"className":3078},[586],[588,3080,3081],{"xmlns":590},[593,3082,3083,3093],{},[596,3084,3085],{},[610,3086,3087,3089,3091],{},[599,3088,614],{},[599,3090,633],{},[619,3092,621],{},[668,3094,3095],{"encoding":670},"r_i^2",[575,3097,3099],{"className":3098,"ariaHidden":644},[675],[575,3100,3102,3105],{"className":3101},[679],[575,3103],{"className":3104,"style":2774},[683],[575,3106,3108,3111],{"className":3107},[688],[575,3109,614],{"className":3110,"style":719},[688,689],[575,3112,3114],{"className":3113},[723],[575,3115,3117,3148],{"className":3116},[727,728],[575,3118,3120,3145],{"className":3119},[732],[575,3121,3123,3134],{"className":3122,"style":2633},[736],[575,3124,3125,3128],{"style":2795},[575,3126],{"className":3127,"style":745},[744],[575,3129,3131],{"className":3130},[749,750,751,752],[575,3132,633],{"className":3133},[688,689,752],[575,3135,3136,3139],{"style":2636},[575,3137],{"className":3138,"style":745},[744],[575,3140,3142],{"className":3141},[749,750,751,752],[575,3143,621],{"className":3144},[688,752],[575,3146,772],{"className":3147},[771],[575,3149,3151],{"className":3150},[732],[575,3152,3154],{"className":3153,"style":2825},[736],[575,3155],{}," ab, nicht ",[575,3158,3160,3182],{"className":3159},[582],[575,3161,3163],{"className":3162},[586],[588,3164,3165],{"xmlns":590},[593,3166,3167,3179],{},[596,3168,3169,3171],{},[599,3170,608],{},[610,3172,3173,3175,3177],{},[599,3174,614],{},[599,3176,633],{},[619,3178,621],{},[668,3180,3181],{"encoding":670},"\\pi r_i^2",[575,3183,3185],{"className":3184,"ariaHidden":644},[675],[575,3186,3188,3191,3194],{"className":3187},[679],[575,3189],{"className":3190,"style":2774},[683],[575,3192,608],{"className":3193,"style":712},[688,689],[575,3195,3197,3200],{"className":3196},[688],[575,3198,614],{"className":3199,"style":719},[688,689],[575,3201,3203],{"className":3202},[723],[575,3204,3206,3237],{"className":3205},[727,728],[575,3207,3209,3234],{"className":3208},[732],[575,3210,3212,3223],{"className":3211,"style":2633},[736],[575,3213,3214,3217],{"style":2795},[575,3215],{"className":3216,"style":745},[744],[575,3218,3220],{"className":3219},[749,750,751,752],[575,3221,633],{"className":3222},[688,689,752],[575,3224,3225,3228],{"style":2636},[575,3226],{"className":3227,"style":745},[744],[575,3229,3231],{"className":3230},[749,750,751,752],[575,3232,621],{"className":3233},[688,752],[575,3235,772],{"className":3236},[771],[575,3238,3240],{"className":3239},[732],[575,3241,3243],{"className":3242,"style":2825},[736],[575,3244],{},{"title":3246,"searchDepth":3247,"depth":3247,"links":3248},"",2,[3249,3250,3251],{"id":561,"depth":3247,"text":562},{"id":1312,"depth":3247,"text":1313},{"id":2428,"depth":3247,"text":2429},[3253,3256,3258,3261,3264,3267,3270],{"lhs":3254,"rhs":3255},"pi*ra^2 - pi*ri^2","pi*(ra^2 - ri^2)",{"lhs":3255,"rhs":3257},"pi*(ra + ri)*(ra - ri)",{"lhs":3259,"rhs":3260},"pi*(5^2 - 3^2)","16*pi",{"lhs":3262,"rhs":3263},"round(16*pi, 2)","50.27",{"lhs":3265,"rhs":3266},"pi*((12\u002F2)^2 - (4\u002F2)^2)","32*pi",{"lhs":3268,"rhs":3269},"round(32*pi, 2)","100.53",{"lhs":3271,"rhs":3272},"pi*(5 - 3)^2","4*pi","r_a > r_i \\geq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>>\u003C\u002Fmo>\u003Cmsub>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r_a > r_i \\geq 0\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:0.6891em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">a\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:0.786em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":3278,"x":3279,"y":3282,"items":3283},"Kreisring zwischen dem äußeren Kreis mit Radius rₐ und dem inneren Kreis mit Radius rᵢ",[3280,3281],-2.6,2.6,[3280,3281],[3284,3507,3511,3514,3520,3525,3529],{"type":3285,"points":3286,"fill":3506},"polygon",[3287,3290,3293,3296,3299,3302,3305,3308,3311,3314,3316,3317,3318,3319,3320,3321,3322,3323,3324,3325,3327,3329,3331,3333,3335,3337,3339,3341,3343,3345,3347,3349,3351,3353,3355,3357,3359,3361,3362,3363,3364,3365,3366,3367,3368,3369,3370,3371,3372,3373,3374,3375,3376,3377,3378,3379,3380,3381,3382,3383,3384,3385,3386,3387,3388,3389,3390,3391,3392,3393,3394,3395,3396,3397,3399,3402,3405,3408,3411,3414,3417,3420,3423,3426,3429,3432,3435,3438,3441,3444,3447,3450,3452,3453,3454,3455,3456,3457,3458,3459,3460,3461,3462,3463,3464,3465,3466,3467,3468,3469,3470,3471,3472,3473,3474,3475,3476,3477,3478,3479,3480,3481,3482,3483,3484,3485,3486,3487,3488,3489,3490,3491,3492,3493,3494,3495,3496,3497,3498,3499,3500,3501,3502,3503,3504,3505],[3288,3289],2.2,0,[3291,3292],2.192,0.192,[3294,3295],2.167,0.382,[3297,3298],2.125,0.569,[3300,3301],2.067,0.752,[3303,3304],1.994,0.93,[3306,3307],1.905,1.1,[3309,3310],1.802,1.262,[3312,3313],1.685,1.414,[3315,3315],1.556,[3313,3312],[3310,3309],[3307,3306],[3304,3303],[3301,3300],[3298,3297],[3295,3294],[3292,3291],[3289,3288],[3326,3291],-0.192,[3328,3294],-0.382,[3330,3297],-0.569,[3332,3300],-0.752,[3334,3303],-0.93,[3336,3306],-1.1,[3338,3309],-1.262,[3340,3312],-1.414,[3342,3315],-1.556,[3344,3313],-1.685,[3346,3310],-1.802,[3348,3307],-1.905,[3350,3304],-1.994,[3352,3301],-2.067,[3354,3298],-2.125,[3356,3295],-2.167,[3358,3292],-2.192,[3360,3289],-2.2,[3358,3326],[3356,3328],[3354,3330],[3352,3332],[3350,3334],[3348,3336],[3346,3338],[3344,3340],[3342,3342],[3340,3344],[3338,3346],[3336,3348],[3334,3350],[3332,3352],[3330,3354],[3328,3356],[3326,3358],[3289,3360],[3292,3358],[3295,3356],[3298,3354],[3301,3352],[3304,3350],[3307,3348],[3310,3346],[3313,3344],[3315,3342],[3312,3340],[3309,3338],[3306,3336],[3303,3334],[3300,3332],[3297,3330],[3294,3328],[3291,3326],[3288,3289],[3398,3289],1.32,[3400,3401],1.315,-0.115,[3403,3404],1.3,-0.229,[3406,3407],1.275,-0.342,[3409,3410],1.24,-0.451,[3412,3413],1.196,-0.558,[3415,3416],1.143,-0.66,[3418,3419],1.081,-0.757,[3421,3422],1.011,-0.848,[3424,3425],0.933,-0.933,[3427,3428],0.848,-1.011,[3430,3431],0.757,-1.081,[3433,3434],0.66,-1.143,[3436,3437],0.558,-1.196,[3439,3440],0.451,-1.24,[3442,3443],0.342,-1.275,[3445,3446],0.229,-1.3,[3448,3449],0.115,-1.315,[3289,3451],-1.32,[3401,3449],[3404,3446],[3407,3443],[3410,3440],[3413,3437],[3416,3434],[3419,3431],[3422,3428],[3425,3425],[3428,3422],[3431,3419],[3434,3416],[3437,3413],[3440,3410],[3443,3407],[3446,3404],[3449,3401],[3451,3289],[3449,3448],[3446,3445],[3443,3442],[3440,3439],[3437,3436],[3434,3433],[3431,3430],[3428,3427],[3425,3424],[3422,3421],[3419,3418],[3416,3415],[3413,3412],[3410,3409],[3407,3406],[3404,3403],[3401,3400],[3289,3398],[3448,3400],[3445,3403],[3442,3406],[3439,3409],[3436,3412],[3433,3415],[3430,3418],[3427,3421],[3424,3424],[3421,3427],[3418,3430],[3415,3433],[3412,3436],[3409,3439],[3406,3442],[3403,3445],[3400,3448],[3398,3289],true,{"type":3508,"from":3509,"to":3510},"segment",[3289,3289],[3288,3289],{"type":3508,"from":3512,"to":3513},[3289,3289],[3425,3424],{"type":3515,"at":3516,"text":3519},"label",[3517,3518],1.76,0.52,"r_a",{"type":3515,"at":3521,"text":3524},[3522,3523],-0.3,0.75,"r_i",{"type":3515,"at":3526,"text":601},[3527,3528],-1.009,-1.442,{"type":3530,"at":3531,"label":3532,"offset":3533},"point",[3289,3289],"M",[3534,3535],-6,16,"\u003Csvg 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dominant-baseline=\"middle\" class=\"fig-label\">r\u003Ctspan class=\"fig-sub\" dy=\"4\">i\u003C\u002Ftspan>\u003C\u002Ftext>\u003Ctext x=\"76.37\" y=\"194.02\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">A\u003C\u002Ftext>\u003Ccircle cx=\"124.8\" cy=\"124.8\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"118.8\" y=\"140.8\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">M\u003C\u002Ftext>\u003C\u002Fsvg>","annulus-area","A = \\pi \\left(r_a^2 - r_i^2\\right)","\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>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>π\u003C\u002Fmi>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmsubsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsubsup>\u003Cmo>−\u003C\u002Fmo>\u003Cmsubsup>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsubsup>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = \\pi \\left(r_a^2 - r_i^2\\right)\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\">A\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:1.2141em;vertical-align:-0.35em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-2.453em;margin-left:-0.0278em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.247em;\">\u003Cspan>\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>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-2.453em;margin-left:-0.0278em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.247em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size1\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Fkreisring",[],[3545,3546,3547],"circle-area","circle-circumference","circular-sector-area",{"title":548,"description":3246},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fkreisring","Die Fläche eines Kreisrings ist die Fläche des äußeren Kreises minus die Fläche des inneren Kreises.",[3552,3553,3554,3555],"kreisring","flächeninhalt","kreis","radius",[3557,3560,3563,3566],{"symbol":601,"meaning":3558,"symbolHtml":3559},"Flächeninhalt des Kreisrings","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A\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\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3519,"meaning":3561,"symbolHtml":3562},"Radius des äußeren Kreises","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r_a\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:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">a\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3524,"meaning":3564,"symbolHtml":3565},"Radius des inneren Kreises (des Lochs)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>r\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">r_i\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:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3567,"meaning":3568,"symbolHtml":3569},"\\pi","Kreiszahl, etwa 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>","v6AAtQngY4vXM07h_twkzjm7CndA7LAjHB6LKx0593E",[3572,3575,3578],{"stem":3573,"title":3574,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fflaecheninhalt-kreis","Flächeninhalt eines Kreises",{"stem":3576,"title":3577,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fkreissektor","Flächeninhalt eines Kreissektors",{"stem":3579,"title":3580,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fumfang-kreis","Umfang eines Kreises",1793824268626]