Use the Shell Method to find the given volume of rotation.

The torus obtained by rotating the circle (x − a)² + y² = b² about the y-axis, where a > b (compare with Exercise 60 in Section 6.3). Evaluate the integral by interpreting part of it as the area of a circle.

Data From Exercise 60 in Section 6.3

The solid generated by rotating the region between the branches of the hyperbola y² − x² = 1 about the x-axis is called a hyperboloid (Figure 16). Find the volume of the hyperboloid for −a ≤ x ≤ a.

Transcribed Image Text:

-a 1 -1 y a -x