Chapter 8.3, Problem 72E

To determine

To find : the volume.

Answer to Problem 72E

The volume is $2a^{2}b{\pi }^2$ .

Explanation of Solution

Given information : The disk $x^2+y^2\le a^2$ is revolved about the line $x=b\left(b>a\right)$ to generate a solid shaped like a doughnut, called a torus.

Calculation :

The volume of torus is the same as the volume of a cylinder, the cylinder has just been rolled into a doughnut shape.

Therefore, the volume is given by the area of the cross section time the height.

The area of the cross section is $\pi a^2$ .

The height is $2\pi b$ .

So, the volume of torus is $2a^{2}b{\pi }^2$ .