For detailed information about sphere, see the Solid Geometry entry, The Sphere.
 

The formula for the volume of the sphere is given by

Example 2
Find the volume generated when the area in Example 1 will revolve about the y-axis.
 

Example 1
Find the volume of the solid generated when the area bounded by the curve y² = x, the x-axis and the line x = 2 is revolved about the x-axis.
 

Solids of Revolution by Integration

The solid generated by rotating a plane area about an axis in its plane is called a solid of revolution. The volume of a solid of revolution may be found by the following procedures: