常用求面积、体积公式86597

1、标准实用1-3 常用求面积、体积公式1-3-1平面图形面积平面图形面积见表1-73平面图形面积表1-73图妙尺寸符号面积(A)1心 G)方形a边长d対人蜿A fl=yA = Q.707rfd = l，414a =1 + 4147在对肃线交点上文案大全d短边b长边d *世角线A - -Jaistr）Ca &、対应角 A、B、C的边艮GD-yHDCO- DA平行四边B在对血饶交点hCE = ABAF = CDa = CD （上底边） bAB （下庇四 hha边 K：K,慕數，i指套边腿的边数f?外接匾半径冃一系数，（拆正多边形的边叢在内接IB心或外 揍團心址人宀P=正三边晤 Kj = 0.433*

2、 Pj=1.29 正四边形 K*=l*(XKh F*-2.ono 正五边Ki = 1.720, P5-2.375 正六边K6=2,59&h Pfi*2.59B 正七边形陷=3.63飢P7-2.736 正八边K, = 4.82Sp Ps-2.828 正九边K-6J83.2.893正十边形Km刃.桶4, P10 = 2.939 正十一边Ku = 9.364. Pm-2.973 正十二边 Kia-1E196T P = 3.0001-3-2多面体的体积和表面积多面体的体积和表面积见表1-74。多面体的体积和表面积表1-74障积（V） 底面积（A）表面积（S）棚表面积（$图 影尺寸符号V = aJS =

3、 6a1Sj = 4a在討角线交点上氐丹阵梭柱O底面对角线交点S = 2 (a*b + a -h + b- hS2h a + A)d =+ bJ + h1V = A*h$ (a 1+ t) * A + 2ASi ( + A + c ) - ftf个级合三角足的一一給合三角殛的个数0厲各对馆线交点S= n*/+ASt = n VAn A?两平齐底面的面积內一底面间的跑硬乜个组合携带的血一坦合梯雜数+ ZiAi)S - tfn + Ai * A】S an51柱和空心K柱(管】R外半轻r内半径 f 注St厚嵐P一平均半疑 虽内外删面駅PttlV nJ?* hS2xRh *2如 吕1 = 2如空心直圜

4、甘：I V = jfh (R=- ra)= 2irRPth5=2jt (fi+ r) A+ 2#xGC = -尺寸符号(V)底面(4)董面积(閃慚表面积心2)斜截育X柱靳Jft小高度h2最大高度r底面半径r球半径圧弓形底園直栓h弓雁窩V=ywr2Ji =2.O944r2ftS =y(4h + a JD一中间断面直艳 d底亀毎一桶高对于枇物线竜幡檢】Yx(2DUm*|洌 对于圜形桶板： =旨1 (2DJ/)在轴交虑上球t +| (I*曲、c半辅S iVlh* J心 * X杞轴交点上暑rWS柱半径1 1阖柱也vfz + G-y在二轴线交点上梯休1 - |盘、b下虑边怏 心、加上底边怏h上、下底边定

5、* (高)V =【(2E05640J79U07980.060E00950.0901,02120.1201.03720.1501.05710.1801.0SQ70,061L.00980.091l+02170J21L03780.1511.05780.181l.om0.0621,01020.0921.02210.1221.03840.1521.05360.1821.08240.0631.01050.0931.02260.123L03900.1551.05950.1B3I*0832Q.Q64E0108A.Q941.02310.1241.03960.154I.06010.1B41.0M10,06S1+0

6、1120.095I+0236OJ251.04020.1551.060B(L1K51.08490.0661.01150.0961.02410.1261,04080.1561.06160.1B6L.0S5SQ.0671hQ1180,0971.02460.1271.041501.06230.1871 0867U,0681.01220.0981.02510.1281,04210.1581,06310.1BS1.08750.0691.01260.0991.02560J291.042&QAS91.06380.1891.08B4(J.0701.01290.100102610.1300J601.06460.

7、1W1 08930,0711,D133U.1U1L,026fr0.1311,04400.1611.06540.1911.U9O20.0721.01370.102L02710.B23.04470.1621.0661(M920.0731.01400.103E02760.1331.04530J631.06600.1931.09190.0741.01440.1041.02S10.1341.Q460Q.1641.067704941 .09280.0751.014B0.105t+02BT0,13S1.04670.1651.06850.1351.09370.0761.01520.1061.02420.136

8、1.04730.1661tQ6930. 1961,0M60.077k01560+1071.02970.1371.04800.1671.07000.1971,09550.07B1.0J60OJ081.03030.1381.04A70.161.0708 0U 981.09&40.079KQ1640.1H9U0SD80,1391.04940.1691.07160.1991.0973查表说明例已知2a = 24.0m , 2b = 16.0m , hx= 3.0m , hy= 2.8m，试求椭圆抛物面扁壳表面积Ao先求出 hx/2a = 3.0/24.0 = 0.125hy/2b = 2.8/16.0

9、 = 0.175分别查表得系数 Ka为1.0402和系数Kb为1.0765，则扁壳表面积 A =24.0 X1.0402 X16.0 X1.0765 = 429.99m 21-3-4-4圆抛物面扁壳（图1-3 ）图1-3圆抛物面扁壳计算图壳面方程式：Z =(X2 + 2)式中 X、Y. Z在壳面上任一点对原点O的坐标; R半径；假设2a一对应弧猛的弦长；2b对应弧赢的弦长；S,弧AGB的长；Sy弧BDC的长；H弓形AGB的高* hy弓形总DC的髙； 弓形AGB的面积；Ay弓形BDC的面枳常 f壳顶到底面距离匸 cAC的长。则：c - 2卫+ f2J?1. 弧长按下式计算Sx = JU + i?

10、 Hn J + 用 +N 片二育 Jr2 + b2 + i In（令 + 寺 JR：Q j2. 壳表面枳按下式计算3. 侧面积按下式计算A = Sj * Sy1-3-4-5 单、双曲拱展开面积1 单曲拱展开面积=单曲拱系数x水平投影面积。2 .双曲拱展开面积=双曲拱系数(大曲拱系数x小曲拱系数)X水平投影面积单、双曲拱展开面积系数见表1-77。单双曲拱展开面积计算图见图1-4图1-4单、双曲拱展开面积计算图L-拱跨；F-拱高单、双曲拱展开面积系数表表1-77lF/L单曲拱 系数1/21/31/41/51/61/71/81/91/10/胞曲1.501.251.151.10E07E051 041,031.020曲拱基数1/21,502,251.8751.725L6501,6051.5751,5691.545l + 5301/31.251.8751.5631.43S13751.3301313E3ft01.2881.2751/4LL51/7251-4531,323L2651.2311.2081 + 1961.1&51.1731/51.101.650t + 3托1.2651.2101.1771.155E1441.1331.1221.071.6051.33?1.231I 1.1771,1451424K1021.D911/71.051.5751*3131