A **Solid of revolution** is a solid formed by the rotation of a function around a line. Many common shapes, such as spheres, cones, and cylinders are solids of revolution. The volume of such a solid can be calculated by using rings or shells, or by using a double integral in the form

assuming the rotation is about the line .

The **surface of revolution** is the surface enclosing the solid. The surface area of a surface of revolution can be found with the formula

## Examples

Find the volume of the solid of revolution obtained when the function

(a semicircle rotated to obtain a sphere) is rotated about the -axis.