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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 unit longer than .