The equations are , ,  and .

Find the volume of the solid generated by revolving the region about the -axis.

The Volume of the solid solid generated by revolving the region about the -axis, for the function  in the interval  is .

Here  and .

The volume of the solid is .

Apply formula : .

The volume of the solid is .

The center of mass:

Let  and  be continuous functions such that  on , and consider the planar lamina of uniform density  bounded by the graphs of  and .

The moments about the -axis and -axis are

.

.

The center of mass  is  and , where  is the mass of the lamina.

Find the centroid of the region.

Here ,  and .

Find .

Substitute,  and   in

.

Substitute  in .

.

Find .

Substitute,  and   in .

.

Find the center of mass .

The center of mass  is  and , where  is the mass of the lamina.

Substitute,  and   in .

Apply formula : .

.

Substitute  and  in  in .

.

Substitute  and .

The centroid of the solid is .

The volume of the solid is  and centroid is .