| 空间情形下旋转体体积的计算 |
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| 引用本文： | 王林芳,马雅琴.空间情形下旋转体体积的计算[J].数学的实践与认识,2006,36(5):304-307. |
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| 作者姓名： | 王林芳 马雅琴 |
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| 作者单位： | 苏州科技学院应用数学系,江苏,苏州,215009 |
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| 摘 要： | 运用定积分中的元素法,给出了空间曲线绕空间直线旋转一周所成的旋转曲面与垂直于旋转轴的两个平面所围成的旋转体体积的计算公式:V=π(m2+n2+p2)23∫tt12{p(y(t)-b)-n(z(t)-c)]2+m(z(t)-c)-p(x(t)-a)]2+n(x(t)-a)-m(y(t)-b)]2}m.x′(t)+n.y′(t)+p.z′(t)dt从而将平面图形的旋转体体积推广到了空间情形.
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| 关 键 词： | 旋转体 体积 曲线 旋转轴 平面 |
| 修稿时间： | 2004年12月6日 |
The Calculation about the Volume of Body of Rotation in Space Situation |
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| WANG Lin-fang,MA Ya-qin.The Calculation about the Volume of Body of Rotation in Space Situation[J].Mathematics in Practice and Theory,2006,36(5):304-307. |
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| Authors: | WANG Lin-fang MA Ya-qin |
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| Abstract: | Using of the element method of the definite integral,this paper gives the calculation formula of the volume of the body of rotation that encircled by the surface of revolution which formed by the space curve rotates the space right line a circle and the two planes which perpendicular the rotation axis: V=π(m~2+n~2+p~2)~~(32)∫~(t_2)_(t_1){p(y(t)-b)-n(z(t)-c)]~2+m(z(t)-c)-p(x(t)-a)]~2+n(x(t)-a)-m(y(t)-b)]~2}|m·x′(t)+n·y′(t)+p·z′(t)|dtSo we extend the volume of the body of rotatoin of the plane figure to that of the space situation. |
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| Keywords: | body of rotation volume curve axis of rotation plane |
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