Volume of a Sphere

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 one-third of the cylinder after the sphere is removed.


Therefore, a sphere is equal to two-third of a cylinder of the same diameter and height.

Here the volume of the cylinder  = 2\pi {r^2} \times 2r = 2\pi {r^3}

\therefore       The volume of the sphere  = \frac{2}{3} \times 2\pi {r^3} = \frac{4}{3}\pi  {r^3}



  1. Volume of a sphere  = \frac{4}{3}\pi {r^3} or \frac{\pi }{6}{d^3}, where r is the radius and d is the diameter of the sphere.
  2. Volume of a hemisphere  = \frac{2}{3}\pi {r^3}