Question

Find the ratio between the volume of a sphere and the volume of the circumscribing right cylinder.

Answer 1

For sphere: Let the radius is equal to $r$.

$\text{Volume of sphere}=\frac{4}{3}\pi r^3$

For circumscribing cylinder:

Radius $=r$

Height $=$ Diameter of the sphere

$=2r$

$\text{Volume of cylinder}=\pi r^2\left(2r\right)$

$=2\pi r^3$

Now, the required ratio will be,

$\frac{\text{Volume of sphere}}{\text{Volume of cylinder}}=\frac{\frac{4}{3}\pi r^3}{2\pi r^3}$

$=\frac{2}{3}\text{or}2:3$