[Calculus] Volume of the Tricylinder
By: Tao Steven Zheng (鄭濤)?
【Problem】
The tricylinder is a solid formed by intersecting three perpendicular cylinders:
Determine the volume of the tricylinder.
【Solution】
Dissect the tricylinder into seven pieces: 1 cube of side length , and 6 congruent “caps“. The integral for calculating the volume of the cap involves integrating the square cross-sections
on the interval
.
The volume of the cube is
The volume of each cap is
Thus, the volume of the tricylinder is
標(biāo)簽：
