三圆柱体垂直相交体积的计算

Volume of the Solid Common to Three Vertically Intersected Cylinders

针对三个直径相同的圆柱体垂直相交所构成的区域,给出求解其体积的积分表达式和积分值,比较不同坐标系下的积分表达式,进一步给出直径不同的三个圆柱体垂直相交所构成的立体体积的积分表达式.

This paper evaluates the volume of the solid common to three vertically interested cylinders by using the triple integral. The case of same diameter cylinders is discussed first. Followed by the comparison of integral expressions in different coordinate systems, the integral expression for the volume of solid common to three different cylinders is obtained.