Question

A cone and a hemisphere have the same base and the same height. Find the ratio between their volumes.

Answer 1

Volume of cone =$\frac{1}{3}\pi r^{2}h$
Volume of hemisphere = $\frac{2}{3}\pi r^3$
Volume of cylinder = $\pi r^{2}h$
Given that cone, hemisphere and cylinder have equal base and same height
That is r = h
Volume of cone : Volume of hemisphere : Volume of cylinder = $\frac{1}{3}\pi r^{2}h$ : $\frac{2}{3}\pi r^3$ : $\pi r^{2}h$
=$\frac{1}{3}\pi r^3$: $\frac{2}{3}\pi r^3$ : $\pi r^3$
= $\frac{1}{3}:\frac{2}{3}:1$
= 1: 2: 3