# How do you use an integral to find the volume of a solid torus?

##### 1 Answer

Aug 30, 2014

If the radius of its circular cross section is

Let's say the torus is obtained by rotating the circular region

By Washer Method, the volume of the solid of revolution can be expressed as:

which simplifies to:

Since the integral above is equivalent to the area of a semicircle with radius r, we have