Question

How to find the volume of a quarter-sphere?

Answer 1

As the word suggests, a quarter-sphere is a quarter of a sphere, and thus the volume of a quarter-sphere is a quarter of the volume of the sphere.

The volume of a sphere is computed as

$\dfrac{4}{3} \pi r^3$

So, the volume of a quarter-sphere is

$\dfrac{1}{4}\cdot \dfrac{4}{3} \pi r^3 = \dfrac{1}{3} \pi r^3$