The volume of the solid is .

Rewrite the integral as .

The volume of the solid using shell method is,

.

Here height is , radius is and thickness is .

The region bounded between the limits and .

Because the thickness that means integrate along the -axis.

(a)

Plane region bounded by equations , and .

(b)

Because the thickness that means integrate along the -axis, and for the shell method, integrating along mean the axis of revolution is the -axis.

(a) Plane region bounded by equations , and .

(b) The axis of revolution is the -axis.