利用形心坐标公式计算旋转体的表面积和体积

在高等数学教学中，一般都用微元法来求解旋转体的体积和表面积。但微元法解题有时相当繁杂，而且计算过程中容易出错。因此，文章从形心的坐标公式出发，结合柱壳法求旋转体体积及侧面积的公式，推证古鲁金定理，最后列举6个例题，说明古鲁金定理的应用。结果表明，用古鲁金定理求旋转体的体积和表面积可以简化计算，提高结果的准确性。

Computing the Volume and Superficial Area of Rotation by Using Centroid Coordinate Formula

In the higher mathematics teaching, Differential method were often used to compute the volumes and the lat- eral areas of the revolutions, but the process may be complicated or the results be prone wrong using this method . In this paper , with the help of formula of centroid coodinate, this paper proves the P. Guldin theorem by using the method of cy- lindric hell which can be used to computing the volumes and the lateral areas of the revolutions. Finally, the paper gives eight examples by using the P. Guldin theorem. The results show that the process can be simplified and the accuracy of re- suits can be improved by using P. Guldin theorem.