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 .