一般旋转体的体积和侧面积计算公式

General Formula for Volume and Area of Lateral Surface of the Solid of Revolution

在一般数学分析教材中,关于旋转体的体积和侧面积的计算都是就旋转体的对称轴是X轴或Y轴这两种特殊情况进行研究的。但实际上,由于曲线y=f(x)经坐标变换后,有时会变得非常复杂,为此提出将微元法和解析法相结合,推出一般旋转体体积和侧面积的计算公式,使这类计算变得简洁明了。

The method of calculation about volume and area of lateral surface of a solid of revolution has been introduced at the present textbook Higher Mathematics, but it only deals with the special cases of a curve ladder-shaped moving round the X-axis （or Y-axis）. This article has given the general formula for volume and area of lateral surface of the solid of revolution by differential method.