Volume of a Sphere

If a sphere is placed in a cylinder of the same diameter and with an height 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-thirds 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. The 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. The volume of a hemisphere $$ = \frac{2}{3}\pi {r^3}$$