Question

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volume is ?

Answer 1

Bases of a cone, hemisphere and a cylinder are same Let radius of each = r
and height of each = r
$\therefore$ Volume of cone $=\frac{1}{3}\pi r^2\times r=\frac{1}{3}\pi r^3$
Volume of hemisphere $=\frac{2}{3}\pi r^3$
and volume of cylinder$=\pi r^2\left(r\right)=\pi r^3$
$\therefore$ ratio in their volumes $=\frac{1}{3}\pi r^3:\frac{2}{3}\pi r^3:\pi r^3=\frac{1}{3}:\frac{2}{3}:1=1:2:3$