The torus (doughnut-shaped solid) in Figure 15 is obtained by rotating the circle (x a) 2

Question:

The torus (doughnut-shaped solid) in Figure 15 is obtained by rotating the circle (x − a)² + y²= b² around the y-axis (assume that a > b). Show that it has volume 2π2ab2. After simplifying it, evaluate the integral by interpreting it as the area of a circle.

a a+b -X