If a sphere is placed in a cylinder of the same diameter and with an altitude equal to the diameter, and the vacant spaces are filled with sand, the sand will be found to fill exactly onethird of the cylinder after the sphere is removed.
Therefore, a sphere is equal to twothird of a cylinder of the same diameter and height.
Here the volume of the cylinder
The volume of the sphere
Summary:

Volume of a sphere or , where is the radius and is the diameter of the sphere.

Volume of a hemisphere