面积、体积计算公式

1、用求面积、体积公式一、平面图形面积甥泰尺寸符号根A）重心（G）正方奉阳.a边长d对角败A=a1a=yA=0.7071fd-1.414a=1.414/a在对增裁文点上除方形E-蚯边xK-1+1A=耳乐在对班战文点t岑Om山J蜜t田配B&dna1*4a*7用日磨工h耀i周长口.G*对应向1A、1B、心的边感A-jjcifrsiihC*_+立t2G=q白LCL*PAa、b-埠1边h特边间的距离A=ftAoAMnaAO13JJ.口工*1粘尸在Mffj雄交盘l:尾3GE-ABA?=6R=CP（匕底边）A=1jHXJ=12.b3arb形6-A/1下庭斗）藕1234十打僮股9甲校J直径Jh_塔Aq需r?Ix

2、d，4=07&Srfz-0.07（5RP2在圆心上pnJR11K.pumi柄眦形8/A-jMrA-A4在主轴支点G上篇照r半径M亚性HmJ的对应中心启A=ja.，一斤产工2MUji.a3Lr1808-与a，9CK时8=告咚CP5弓形二3；华禽+T*（嵩即立）去匚rJ-b）*MiJm=r*oB-tz五0，175kb1NIJ1启.r-84，当a=1MO”对8.芸.。i一瓠性A-中心向*5区A商fra形尺寸符号面积(A)重心(G)圆环R外半径r内半径D外直径d内直径A=k(R2-r2)彳(D2-c/2)在圆心OT-4苗。R外半径r内半径D外直径d内直径Ra圆环平均半径/环宽A=舞(R2-r2)JOU

3、R3-尸878.2asin蜉=180Rw，2x-旦2新月形OO=L阚心间的跑离j古招人=小一面+如。)=rPjt-rrrasina5G-2paAtZ180P值见下表L且101010空1010纭101A10鼠10乳10p10.400.791.181.561.912.252.552.813.02邙线b底边h高1曲线长Vb21.3333k2A=tb9h形404+SAABC的面积等边多0a边长Ki系效，i指多边形的边数R外接圆半径P.系数.i指正多边形的边数A尸K2=rr2正三边形Kj=0.433,P3=1.299正四边形K4=l.000.P42.000正五边形Ksl.720.Ps=2.375正六边形

4、K.=2.598.P6-2.598正七边形Kk3.634.P产2.736在内接圆心或外边正八边形K.=4.828.Ps=2.828接吸心处形正九边形Kg=6.182,Pg=2.893正十边形Ko=7.694.P10=2.939正十一边形Kii=9.364.Pji=2.973正十二边形Ki2=ll196,Pu=3.000二、多面体的体积和外表积91尺寸符号体积(V)底面积(A)或面帜恻表药眼(SD亶心(G)立方体a枝d-一对甭缓S-表面积Si他表面枳V=aJS5/在对角线交点上(W-长方体(粳柱)%h*b、h边民0底面对角蝴交点a如fiS=2(u*b+a*h+b*hS)=2A(u+ft)QOqd

5、=J+#+A)口、b.cs一边长h11高A底面积0底面中线的交点V=AhS=(&+B+。)*h+2ASi-(a+A+j),hGO-y)极辕Li/个组合三角形的面积n-组合三南形的个数0糜底务对角线交点gA百S,才/十兑Si二GO=-q根台Z露41、Ai-一两平行度面的面枳h底面间的距离a个蛆合樵形的面枳一型合悌形数V=-1-A(Aj+Aj+，再月，S=a“+41+A工S=an8=生x22，久”3A2+yAA；+AjR-外半程r内半径t一柱基厚度P平拗半径Si-内外恻面积ttlV=jrRi-hSu2vRh*2kR2S2*Rh空心直面柱.V=irh(R1-r2)2RPth5-2r(R+r)A+2r

6、X/?2-ra)S1=2jt(R+r)hU11十斗3斜截宜四柱尺寸符号体积（V）底面积（A）表面积（S）则表面积（S。心(G)hi最小高度A2最大高度r底面半径211+2V=l%，5=xr(hi+Aj)+kt2XW)Si=rr(Ai+Aj)go=74+_IHq4(A|+fcj)球扁形(球噢)r球半径d弓形底西直法h弓形高V=yicr2A=2.0944r2/iS=y(4h+d)=1.57r(4hh球缺的高r球缺半径d平切圈直径Su曲面面积S球缺表面积St-2fcrh=S-Kh(4r-A)d2=4h(2r-A)GO号警邛43r-A图形尺寸符号体枳(V)底面积(A)表面积(S)侧表面积(S1)重心(

7、G)圆环体1JR一圆环体平均半径D圆环体平均直径dCE环体截面直径r一圆环体域面半径*V=2/Rr?工入彻24S=4/Rr=MEW=39.478Rr在环中心上L凸1r尸1、厂2底面半径h展高h球心O至惜底IM心O|的距离V=y(3r?+3r|+ft2)S=2xRhS=2nRh*nrj)GO=h+上楠形JafPD中间断面直径d底直径对于抛物线形桶板1V=15x(2DaDd+y2)在轴交点上1桶高对于图形桶板：V哇M(2D2+/)I.4-J4.球体1La、b、c半轴V=abcnS=2久6Ja+b，在轴交点上bLr圜柱半径V=mln+=m2o式中ci=J1十4启c2=J/+46bm2lhv或者二九二

8、2。X系数Ka6,二2bK系数Kb式中系数K八%可分别根据N2的值，查表1-76得到。2口2b2,壳表面积按下式计算A=SjSy3-侧面积按下式计算=不。*h工-,A4LLAy二铲*33、椭圆抛物面扁壳系数计算见图1-2,壳外表积A计算公式:A=SxSy=2ax系数Kax2bx系数Kb式中Ka、Kb椭圆抛物面扁壳系数，可按表查得。椭圆抛物面扁壳系数表扣寸心2a2b系数K,或KhAa寸仆U2b系政K.或占区或江果散K.或心翡噬系数K.或长旨lalb系#nK.或Kl0,0501.00660.0801.01680.1101,03140.1401.05000U7fl1.07240.0511.00690

9、.0811.01720.1111.03200.141K05070371LD7330,0321,00720.0821*017了0J121,03250.1421.05140J721.07410.0531.00740.083L,01Hl0.113L03310.1431.05210.1721.07490,0341.00770.084L01850.1140.1441,05280.1741.07S70.0551.00800.0851.01S90.1151.03420.1451.05350.1751.07650.056U00S30.0S61.01940.1161,03480.1461,05420.1761.

10、07730.0571.00860.0871.01980.1171.03540.1471.05500.177L07820,0男1,00890.08E1.02030,1181,036。0.1481.05570J781.07900.059U009213070.1191.0366C.1491.05640J79UD7980.0601.00950.0901,02120.1201.03720.1501.0571Q.l的1则0.0611.00980.091L02170.1211,0378Q.1511.05780.1811S8150.0621,01020.0921,02210.1221.03840.1521.0

11、5B60.182L08240,0631.01050.095LD2260.123Ltmo0.1531Q5930.183L08320.0641.01080.0941,02310.1241,03960.1541,0601O.IMt0$41G.0651.0112U.095L02360.1251.04020.1551.U60S(LtB5IJ1K490.066141150.0961,02410.1261,04080.1561.06160.1861.08580.0671.01180.097L02460.1271.04150.1571.06230.1S71.08670.0681.01220.0981.0251

12、0.1281,042103581,06310.1(WJ1.08750,0691.01260.0991+02560.1291.042B(M591.06380.189L08S40.070I.01290.1001.02610.1301&340.1601.0646O.L究LUS930,071LU133(J.101L026&0.1311,044003611.06540.191UU9020.072L01370.102L02710.1323.04470.1621.06611.09100,073I.C1400.1031,02760,1331,04330J631.0669QJ93109190.0741.0144

13、0.104U02&10.1341.04600.1641.0677DJ941.09280.075L01480.105L0207O.1351.046703651.06850J951.0370.0761.01520.!06U029203361.04730.1661.06930.1961.09460,077L01S60.1U71.029703371.04800.1C7L07000J97L09S50.0781.01600JO8U03D3Q.I3B1.04A70.网1.Q7O00.1州1.09M0.079K01640.109U03080,1391,04940.1691.07160499i.ora查表说明例

14、已知2a=24.0m,2b=16.0m,hx=3.0m,hy=2.8m,试求椭圆抛物面扁壳外表积A先求出hxhy分别查表得系数KabXX夹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:(Xa+Y1)ZjK式中x、y、z在壳面上任一点对原点。的坐标；R半径；假设2a对应弧AGB的弦长;2b对应弧EDC的弦长i5H瓠AGE的长：Sy弧EDC的长：hx弓形AGB的高*hy弓形BDC的高；4Klp弓形AGB的面积；Ay弓形BDC的面积；f壳顶到底面距离；cAC的长0则：C=22K=2R如二市1 .弧长按下式计算Sk=/Jr2+a2+rin；Jr2+公,1Jr2+M+j?in+/r2+7

15、)2,壳表面积按下式计算A=SK1Sr3 .侧面积按下式计算.2a34,A一正二才加八2b4.%=支=”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1-4单、双曲拱展开面积系数见表1-77o单双曲拱展开面积计算图见图图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1-77单曲拱系数F/L1/21/31/41/51/61/7l/S1/91/10f/l单曲拱系教L5011/251.151,10L07LOS1.0$1,0311.02双曲拱系数1/21/31/4V51/61/71/81/91/101.50L251.151301.071.0513L03Eft：2.251.8751/7251.6501.6051.575LS6OL54511Po1*8751.5631.4331+3”l.TO1.3131.3001.2881.2751.7251.4381323L2651.2311-2031.1961.1851.1731.6501.375