数学一些重要体积、面积公式、高中
\u6570\u5b66\u6c42\u4f53\u79ef\u3001\u9762\u79ef\u7684\u6240\u6709\u516c\u5f0f\u5e73\u9762\u56fe\u5f62:
\u957f\u65b9\u5f62 S=ab \u9762\u79ef=\u957f*\u5bbd
\u6b63\u65b9\u5f62 S=aa \u9762\u79ef=\u8fb9\u957f*\u8fb9\u957f
\u5e73\u884c\u56db\u8fb9\u5f62 S=ah \u9762\u79ef=\u5e95*\u9ad8
\u4e09\u89d2\u5f62 S=ah/2 \u9762\u79ef=\u5e95*\u9ad8/2
\u68af\u5f62 S=(a+b)h/2 \u9762\u79ef=(\u4e0a\u5e95+\u4e0b\u5e95)*\u9ad8/2
\u7acb\u4f53\u56fe\u5f62:
\u957f\u65b9\u4f53 V=abh \u4f53\u79ef=\u957f*\u5bbd*\u9ad8
S=(ab+ah+bh)*2 \u8868\u9762\u79ef=(\u957f*\u5bbd+\u957f*\u9ad8+\u5bbd*\u9ad8)*2
\u6b63\u65b9\u4f53 V=aaa \u4f53\u79ef=\u68f1\u957f*\u68f1\u957f*\u68f1\u957f
S=6aa \u8868\u9762\u79ef=\u68f1\u957f*\u68f1\u957f*6
\u5706\u8868\u9762\u79ef
S=4*pi*(R^2) S \u8868\u9762\u79ef pi \u5706\u5468\u7387 R\u5706\u76f4\u5f84 ^2 \u5e73\u65b9
\u4f53\u79ef
V=4/3*pi*(R^3) V \u4f53\u79ef pi \u5706\u5468\u7387 R\u5706\u76f4\u5f84 ^3 \u7acb\u65b9
\u7403\u4f53\u79ef\u516c\u5f0f\uff1aV\uff1d4\u03c0R³/3
\u5706\u67f1\u8868\u9762\u79ef
\u8868\u9762\u79ef=\u4fa7\u9762\u79ef+2\u4e2a\u5e95\u9762\u79ef
\u4fa7\u9762\u79ef=\u5e95\u9762\u5468\u957f*\u9ad8=3.14*\u76f4\u5f84*\u9ad8=3.14*\u534a\u5f84*2*\u9ad8
\u5e95\u9762\u79ef=3.14*\u534a\u5f84*\u534a\u5f84
----------------
\u4f53\u79ef=\u5e95\u9762\u79ef*\u9ad8
\u5706\u67f1\u7684\u4f53\u79ef=\u6d3e\uff083.14159265358979\uff09\u00d7\u5e95\u9762\u534a\u5f84\u7684\u5e73\u65b9\u00d7\u5706\u67f1\u7684\u9ad8
\u5706\u67f1\u5e95\u9762\u534a\u5f84r\uff0c\u9ad8\u662fh
\u5706\u67f1\u4f53\u79ef\uff1d\u5706\u5468\u7387\u00d7\u534a\u5f84\u7684\u5e73\u65b9\u00d7\u9ad8
\u6216\u5706\u67f1\u4f53\u79ef\uff1d\u5e95\u9762\u79ef\u00d7\u9ad8
\u5b57\u6bcd\u516c\u5f0f\uff1a
V\uff1dSh
\u5706\u67f1\u8868\u9762\u79ef=\u4e8c\u5e95\u9762\u79ef+\u4fa7\u9762\u79ef
\u5b57\u6bcd\u516c\u5f0f\uff1a
S\u8868\uff1d2S\u5e95+S\u4fa7 = \u5706\u5468\u7387\u00d7\u534a\u5f84\u7684\u5e73\u65b9\u00d72 + 2\u00d7\u5706\u5468\u7387\u00d7r\u00d7h
\u5706\u9525\u8868\u9762\u79ef: \u5706\u5468\u7387 \u00d7r\u00d7\u6bcd\u7ebf+ \u5706\u5468\u7387 \u00d7r\u7684\u5e73\u65b9
\u5706\u9525\u4f53\u79ef\uff1a 3\u5206\u4e4b1 \u00d7 \u5706\u5468\u7387 \u00d7r\u7684\u5e73\u65b9\u00d7 \u5706\u9525\u7684\u9ad8
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\u7ed9\u4f60\u52a0\u4e0a\u4e86\u9ad8\u4e2d\u4e86
\u957f\u65b9\u5f62=\u957f*\u5bbd
\u5e73\u884c\u56db\u8fb9\u5f62=\u957f*\u9ad8
\u4e09\u89d2\u5f62=\u957f*\u9ad8/2
\u6b63\u65b9\u5f62=\u8fb9\u957f*\u8fb9\u957f
\u5706=\u5706\u5468\u7387*\u534a\u5f84\u7684\u5e73\u65b9
\u8fd9\u4e9b\u662f\u5c0f\u5b66\u7684,\u6211\u5df2\u7ecf\u6316\u7a7a\u5fc3\u601d\u4e86,
\u6211\u662f\u516d\u5e74\u7ea7\u7684
\u53c8\u627e\u4e86\u4e00\u4e9b:
\u6211\u7ed9\u7684\u786e\u5b9e\u662f\u521d\u4e2d\u7684\u6570\u5b66\u5b9a\u7406\u548c\u516c\u5f0f\u5927\u5168\uff0c\u697c\u4e3b\u770b\u4e0d\u61c2\u95ee\u9898\u4e0d\u5728\u8fd9\u91cc\uff0c\u5efa\u8bae\u697c\u4e3b\u5148\u4ece\u57fa\u7840\u77e5\u8bc6\u6293\u8d77\uff0c\u5149\u8bb0\u516c\u5f0f\u800c\u4e0d\u7406\u89e3\u662f\u4e0d\u884c\u7684\uff0c\u4ecb\u7ecd
\u51e0\u4e2a\u521d\u4e2d\u751f\u5b66\u4e60\u7f51\u7ad9\u521d\u4e2d\u6570\u5b66\u8d44\u6e90\u7f51
http://www.1230.org/
\u521d\u4e2d\u6570\u5b66\u7f51
http://www.czsx.com.cn/
\u521d\u4e2d\u6570\u5b66\u4e50\u56ed
http://www.0618.org/
\u534e\u5e08\u5927\u521d\u4e2d\u6570\u5b66\u7f51\u7ad9
http://www.hsdczsx.com/Article_Index.asp
\u4e2d\u5b66\u6570\u5b66\u9898\u5e93
http://www.tiku.net/
\u8fd9\u662f\u521d\u4e2d\u7684\u4ee3\u6570\u516c\u5f0f\uff1a
http://www.edu3g.com/math/expressions/czds/index1.html
\u521d\u4e2d\u6570\u5b66\u5e38\u7528\u516c\u5f0f\uff1a
http://edu.northeast.cn/system/2006/09/11/050545772.shtml
\u521d\u4e2d\u6570\u5b66\u516c\u5f0f\uff0c\u8fd9\u4e2a\u9700\u8981\u4e0b\u8f7d\uff1a
http://www.hnmaths.com/Soft/czsx/200605/693.html
\u5e38\u7528\u6570\u5b66\u516c\u5f0f\u8868\uff1a
http://www.wen8.net/html/307.htm
http://forum.heftyedu.com/viewthread.php?tid=740
\u5177\u4f53\u7684\u516c\u5f0f
http://www.ggjy.net/xspd/xsbk/200408/815.html
\u9ad8\u4e2d\u6570\u5b66\u516c\u5f0f\u5927\u5168
http://www.xyjy.cn/Article/UploadFiles/200510/20051013100307519.doc
正方形的周长=边长×4
长方形的面积=长×宽
正方形的面积=边长×边长
三角形的面积=底×高÷2
平行四边形的面积=底×高
梯形的面积=（上底+下底）×高÷2
直径=半径×2
半径=直径÷2
圆的周长=圆周率×直径=
圆周率×半径×2
圆的面积=圆周率×半径×半径
长方体的表面积=
（长×宽+长×高＋宽×高）×2
长方体的体积
=长×宽×高
正方体的表面积=棱长×棱长×6
正方体的体积=棱长×棱长×棱长
圆柱的侧面积=底面圆的周长×高
圆柱的表面积=上下底面面积+侧面积
圆柱的体积=底面积×高
圆锥的体积=底面积×高÷3
长方体（正方体、圆柱体）
的体积=底面积×高
平面图形
名称
符号
周长c和面积s
正方形
a—边长
c＝4a
s＝a2
长方形
a和b－边长
c＝2(a+b)
s＝ab
三角形
a,b,c－三边长
h－a边上的高
s－周长的一半
a,b,c－内角
其中s＝(a+b+c)/2
s＝ah/2
＝ab/2·sinc
＝[s(s-a)(s-b)(s-c)]1/2
＝a2sinbsinc/(2sina)
四边形
d,d－对角线长
α－对角线夹角
s＝dd/2·sinα
平行四边形
a,b－边长
h－a边的高
α－两边夹角
s＝ah
＝absinα
菱形
a－边长
α－夹角
d－长对角线长
d－短对角线长
s＝dd/2
＝a2sinα
梯形
a和b－上、下底长
h－高
m－中位线长
s＝(a+b)h/2
＝mh
圆
r－半径
d－直径
c＝πd＝2πr
s＝πr2
＝πd2/4
扇形
r—扇形半径
a—圆心角度数
c＝2r＋2πr×(a/360)
s＝πr2×(a/360)
弓形
l－弧长
b－弦长
h－矢高
r－半径
α－圆心角的度数
s＝r2/2·(πα/180-sinα)
＝r2arccos[(r-h)/r]
-
(r-h)(2rh-h2)1/2
＝παr2/360
-
b/2·[r2-(b/2)2]1/2
＝r(l-b)/2
+
bh/2
≈2bh/3
圆环
r－外圆半径
r－内圆半径
d－外圆直径
d－内圆直径
s＝π(r2-r2)
＝π(d2-d2)/4
椭圆
d－长轴
d－短轴
s＝πdd/4
立方图形
名称
符号
面积s和体积v
正方体
a－边长
s＝6a2
v＝a3
长方体
a－长
b－宽
c－高
s＝2(ab+ac+bc)
v＝abc
棱柱
s－底面积
h－高
v＝sh
棱锥
s－底面积
h－高
v＝sh/3
棱台
s1和s2－上、下底面积
h－高
v＝h[s1+s2+(s1s1)1/2]/3
拟柱体
s1－上底面积
s2－下底面积
s0－中截面积
h－高
v＝h(s1+s2+4s0)/6
圆柱
r－底半径
h－高
c—底面周长
s底—底面积
s侧—侧面积
s表—表面积
c＝2πr
s底＝πr2
s侧＝ch
s表＝ch+2s底
v＝s底h
＝πr2h
空心圆柱
r－外圆半径
r－内圆半径
h－高
v＝πh(r2-r2)
直圆锥
r－底半径
h－高
v＝πr2h/3
圆台
r－上底半径
r－下底半径
h－高
v＝πh(r2＋rr＋r2)/3
球
r－半径
d－直径
v＝4/3πr3＝πd2/6
球缺
h－球缺高
r－球半径
a－球缺底半径
v＝πh(3a2+h2)/6
＝πh2(3r-h)/3
a2＝h(2r-h)
球台
r1和r2－球台上、下底半径
h－高
v＝πh[3(r12＋r22)+h2]/6
圆环体
r－环体半径
d－环体直径
r－环体截面半径
d－环体截面直径
v＝2π2rr2
＝π2dd2/4
桶状体
d－桶腹直径
d－桶底直径
h－桶高
v＝πh(2d2＋d2)/12
(母线是圆弧形,圆心是桶的中心)
v＝πh(2d2＋dd＋3d2/4)/15
(母线是抛物线形)
数学工式手册里比较全面,可以去买一本.S锥=丌rL+丌r^2 V锥=(1/3)Sh正棱锥也属锥体S柱=2丌r^2+丌rL,其中L都为展开图的母线.V柱=Sh.
你花五块钱,买本公式书,上面高中所有的重要公式都有.~~~
第一轮复习用书上有。
第一轮复习
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