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
Find the volume of the solid of revolution obtained when the function
(a semicircle rotated to obtain a sphere) is rotated about the -axis.