Question

A sphere is inscribed in a cylinder than find the ratio of volume of sphere to volume of cylinder.

Answer 1

A sphere is inscribed in a cylinder

here height of cylinder $h=2r$

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

and Volume of cylinder $=\pi r^{2}h$

$\begin{array}{c}=\pi r^2\left(2r\right)\\ =2\pi r^3\end{array}$

Ratio of volume of sphere to volume of cylinder $=\frac{4\pi r^3}{3\times 2\pi r^3}=2:3$