The curve equation is .

and

(a) Rotation about the -axis.

Disk method:

If  is the volume of the solid of revolution determined by rotating the continuous function  on the interval about the -axis, then .

Solution of the above equations is and .

Partial decomposition of .

.

(b) Rotation about the -axis.

The height of the cylindrical shell is .

Volume of the cylindrical shell is,

Assume .

.

(a) cubic units.

(b) cubic units.