The curve equations are .

Shell method:

The plane region is revolving about the -axis.

The volume of the solid is .

Observe the figure:

On interval :

The distance from the center of the rectangle to the axis of revolution is .

The height of the rectangle is .

On interval :

The distance from the center of the rectangle to the axis of revolution is .

The height of the rectangle is .

Evaluate the integral .

Apply formula: .

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