计算体积 一个穹顶的体积，形状是小半个球体，圆的直径是4.1米，圆的底面到顶高度是1.6米，求体积

\u600e\u6837\u8ba1\u7b97\u7403\u5f62\u7684\u4f53\u79ef

\u7403\u4f53\u7684\u4f53\u79ef\u516c\u5f0f\uff0c\u9996\u5148\u8981\u77e5\u9053\u5b9a\u7406\uff0c\u4e24\u4e2a\u7b49\u9ad8\u7684\u7acb\u4f53\u5f62\u72b6\uff0c\u5982\u679c\u6240\u6709\u76f8\u540c\u9ad8\u5ea6\u7684\u6a2a\u622a\u9762\u79ef\u90fd\u76f8\u7b49\uff0c\u90a3\u4e48\u8fd9\u4e24\u4e2a\u7acb\u4f53\u5f62\u72b6\u7684\u4f53\u79ef\u5c31\u76f8\u7b49\u3002\u975e\u5e38\u5f62\u8c61\u7684\u4f8b\u5b50\uff0c\u5c31\u662f\u53d6\u4e00\u645e\u7eb8\u6216\u8005\u4e00\u645e\u4e66\uff0c\u6574\u6574\u9f50\u9f50\u53e0\u6210\u957f\u65b9\u4f53\u5f62\u72b6\u4e4b\u540e\uff0c\u63a8\u51fa\u4e00\u5b9a\u7684\u659c\u89d2\uff0c\u4f53\u79ef\u5e76\u6ca1\u6709\u53d1\u751f\u53d8\u5316\uff0c\u5c31\u56e0\u4e3a\u76f8\u540c\u9ad8\u5ea6\u90a3\u5f20\u7eb8\u6216\u8005\u90a3\u672c\u4e66\u7684\u9762\u79ef\u6ca1\u6709\u53d8\u5316\u3002

\u6b63\u5982\u5c0f\u5b66\u5b66\u4e60\u5706\u9525\u4f53\u7684\u4f53\u79ef\uff0c\u8981\u9996\u5148\u770b\u770b\u7b49\u5e95\u7b49\u9ad8\u7684\u5706\u67f1\u4f53\uff0c\u6211\u4eec\u8ba1\u7b97\u7403\u4f53\u7684\u4f53\u79ef\uff0c\u5c31\u4e5f\u662f\u5148\u770b\u770b\u7403\u4f53\u7684\u5916\u63a5\u5706\u67f1\u4f53\uff0c\u5e95\u9762\u534a\u5f84\u5c31\u662f\u7403\u7684\u534a\u5f84 R\uff0c\u9ad8\u5c31\u662f\u7403\u7684\u76f4\u5f84 d\uff0c\u8fd9\u6837\u4e00\u6765
V \u5916\u63a5\u5706\u67f1 = 3.14 R" d = 2 X 3.14 R^3

\u6bd5\u7adf\u7403\u662f\u5bf9\u79f0\u7684\u7acb\u4f53\u5f62\u72b6\uff0c\u4f53\u79ef\u6211\u4eec\u5c31\u5148\u770b\u534a\u4e2a\u7403\u3001\u9ad8\u7b49\u4e8e\u534a\u5f84 R \u7684\u5916\u63a5\u5706\u67f1
V \u5706\u67f1 = 3.14 R^3
\u518d\u770b\u770b\u7b49\u5e95\u7b49\u9ad8\u7684\u5706\u9525\u4f53\uff0c\u4f53\u79ef\u662f (1/3) 3.14 R^3 \u3002\u63a5\u4e0b\u6765\u6211\u4eec\u5c31\u770b\u770b\uff0c\u8fd9\u4e2a\u5706\u67f1\u4e0e\u5706\u9525\u7684\u4f53\u79ef\u5dee\uff0c\u5c31\u7b49\u4e8e\u8fd9\u534a\u4e2a\u7403\u7684\u4f53\u79ef\u3002

\u60f3\u8c61\u4e00\u4e0b\u513f\uff0c\u5706\u67f1\u4f53\u4ece\u4e0a\u9762\uff0c\u5012\u7acb\u5730\u62ff\u8d70\u4e2d\u95f4\u7684\u5706\u9525\u4f53\u3002\u8fd9\u6837\u4e00\u6765\uff0c\u9664\u4e86\u6700\u4e0b\u8fb9\u7684\u5e95\u9762\u662f\u5b8c\u6574\u7684\u5706\u5f62\uff0c\u9762\u79ef\u662f 3.14R" \uff0c\u4e2d\u95f4\u6bcf\u4e00\u4e2a\u9ad8\u5ea6\u7684\u622a\u9762\uff0c\u5c31\u90fd\u53ea\u5269\u73af\u5f62\u4e86\u3002\u73af\u5f62\u9762\u79ef\u662f 3.14(R" - r" )\uff0c\u5916\u5706\u9762\u79ef\u51cf\u53bb\u5185\u5706\u9762\u79ef\uff0c\u56e0\u4e3a\u8fd9\u4e2a\u5706\u67f1\u548c\u5706\u9525\u90fd\u662f\u9ad8\u7b49\u4e8e\u5e95\u9762\u534a\u5f84\uff0c\u6bcf\u4e2a\u9ad8\u5ea6\u7684\u73af\u5f62\u622a\u9762\u7684\u9762\u79ef\uff0c\u5c31\u90fd\u662f 3.14(R" - h" )

\u518d\u770b\u770b\u534a\u4e2a\u7403\u4f53\uff0c\u6700\u4e0b\u8fb9\u6700\u5927\u7684\u5e95\u9762\u4e5f\u662f\u5b8c\u6574\u7684\u5706\u5f62\uff0c\u9762\u79ef 3.14R" \uff0c\u6a2a\u622a\u9762\u8d8a\u5347\u9ad8\uff0c\u5706\u5f62\u534a\u5f84 r \u8d8a\u5c0f\uff0c\u9762\u79ef 3.14r" \u8d8a\u5c0f\u3002\u60f3\u60f3\u52fe\u80a1\u5b9a\u7406\uff0c\u540c\u6837\u7684\u9ad8\u5ea6\uff0c\u622a\u9762\u5706\u7684\u534a\u5f84\u7b49\u4e8e\u4ec0\u4e48\uff1fr" = R" - h" \uff0c\u8fd9\u6837\u770b\u51fa\u6765\u6ca1\u6709\uff1f\u8fd9\u534a\u4e2a\u7403\u7684\u4f53\u79ef\uff0c\u5c31\u6b63\u7b49\u4e8e\u8fd9\u4e2a\u5706\u67f1\u548c\u5706\u9525\u7684\u4f53\u79ef\u5dee\uff0c\u662f (2/3) 3.14 R^3 \uff0c\u5982\u679c\u662f\u6574\u4e2a\u7403\uff0c\u4f53\u79ef\u5c31\u662f\u4e24\u500d\u3002
V \u7403 = (4/3) 3.14 R^3

\u7b2c\u4e00\u9898\uff1a
\u8bbe\u5c55\u5f00\u56fe\u7684\u534a\u5f84\u4e3aR\uff0c\u5706\u9525\u7684\u5e95\u9762\u534a\u5f84\u4e3ar\uff0c\u5219
(1/2)\u03c0R²+\u03c0r²=a
2\u03c0R\uff081/2\uff09=2\u03c0r
\u89e3\u5f97r=\u221a\uff08a/3\u03c0\uff09
\u6240\u4ee5\u5706\u9525\u7684\u5e95\u9762\u76f4\u5f84\u4e3a2r=2\u221a\uff08a/3\u03c0\uff09

\u7b2c\u4e8c\u9898\uff1a
\u8bbe\u6c14\u7403\u7684\u534a\u5f84\u4e3ar\uff0c
\u5219\u6c14\u7403\u7684\u4f53\u79ef\u4e3a\uff084/3\uff09\u03c0r³
\u534a\u5f84\u6269\u5927\u4e00\u500d\u540e\u5219\u4e3a2r
\u6b64\u65f6\u7684\u4f53\u79ef\u4e3a\uff084/3\uff09\u03c0\uff082r\uff09³=8\uff084/3\uff09\u03c0r³
8\uff084/3\uff09\u03c0r³\u00f7\uff084/3\uff09\u03c0r³=8
\u5373\u5b83\u7684\u4f53\u79ef\u6269\u5927\u5230\u539f\u6765\u76848\u500d

\u7b2c\u4e09\u9898\uff1a
\u8bbe\u7403\u7684\u534a\u5f84\u4e3ar\uff0c\u56e0\u4e3a\u6b63\u65b9\u5f62\u7684\u9876\u70b9\u90fd\u5728\u7403\u9762\u4e0a
\u5219\uff08a/2\uff09²+[\uff08a/2\uff09²+\uff08a/2\uff09²]=r²
\u89e3\u5f97r=\uff08\u221a3/2\uff09a
\u6240\u4ee5\u7403\u7684\u9762\u79ef\u4e3a\uff084/3\uff09\u03c0r³=\uff084/3\uff09\u03c0[\uff08\u221a3/2\uff09a]³=(\u221a3/2)\u03c0a³

~\u5982\u679c\u4f60\u8ba4\u53ef\u6211\u7684\u56de\u7b54\uff0c\u8bf7\u53ca\u65f6\u70b9\u51fb\u3010\u91c7\u7eb3\u4e3a\u6ee1\u610f\u56de\u7b54\u3011\u6309\u94ae~
~\u624b\u673a\u63d0\u95ee\u8005\u5728\u5ba2\u6237\u7aef\u53f3\u4e0a\u89d2\u8bc4\u4ef7\u70b9\u3010\u6ee1\u610f\u3011\u5373\u53ef\u3002
~\u4f60\u7684\u91c7\u7eb3\u662f\u6211\u524d\u8fdb\u7684\u52a8\u529b~~
~\u5982\u8fd8\u6709\u65b0\u7684\u95ee\u9898\uff0c\u8bf7\u53e6\u5916\u5411\u6211\u6c42\u52a9\uff0c\u7b54\u9898\u4e0d\u6613\uff0c\u656c\u8bf7\u8c05\u89e3~~
O(\u2229_\u2229)O\uff0c\u8bb0\u5f97\u597d\u8bc4\u548c\u91c7\u7eb3\uff0c\u4e92\u76f8\u5e2e\u52a9
\u795d\u5b66\u4e60\u8fdb\u6b65\uff01

球冠体积计算公式:（1/3)π(3R-h)*h^2 二、H=球缺高 R=球半径 A=球缺底半径

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