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.


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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}

 

Summary:


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  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}