### Home > APCALC > Chapter 8 > Lesson 8.1.6 > Problem 8-58

8-58.

Suppose the region in problem 8-56 is revolved around the line instead of the

*-axis. Set up and evaluate a new integral that will calculate the volume of the solid.*

Like problem 8-55, the rotating radius will be horizontal (because the axis of rotation is vertical). Consequently, the bounds of integration will be -values: from

*to*

*. Both the bounds and the integrand will be written in terms of*

*.*

Unlike problem 8-55, there will be a cylindrical hole in the center of this 3D figure. This hole has a radius of

Unlike problem 8-55, the outer function is no longer . It is

*.*