旋转体的体积计算

The Volume Calculation for the Rotating Bodies

旋转体的体积是数学分析中定积分的重要应用之一,关于曲线绕任意直线所成的旋转体的体积的计算公式已有相关文献利用“微元法”思想进行了讨论。在此基础上,本文利用坐标变换的方法对于空间一般曲线绕直线旋转而成的旋转体体积的计算进行了研究,得出了空间一般曲线绕直线旋转一周而成的旋转体的体积公式。

The volume of a rotating body is one of the important applications in mathematical analysis. The calculation formula of the volume of a rotating body formed by a curve around an arbitrary straight line has been discussed in related literatures by using the idea of “micro element method”. Based on this, we use the coordinate transformation to study the calculation of the volume of the revolving body formed by the space general curve rotating around a straight line and obtain the volume formula of the revolving body formed.