# 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 $= \frac{2}{3} \times 2\pi {r^3} = \frac{4}{3}\pi {r^3}$

Summary:

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 $= \frac{2}{3}\pi {r^3}$