Step 1 : \ \

The curve equations are ,  and .

Cylindrical shells method:

The volume of the solid obtained by rotating about the -axis the region under the curve is

.

Find the point of intersections.

Substitute in .

Now we integrate over the interval 0 to 4.

Let us assume the volume of the solid is obtained by rotating about -axis.

Consider .

Volume of the solid obtained by rotating about the -axis the region under the curve and   is

.

Solution : \ \

The volume of the solid is .