Question

$\text{A cone and a hemisphere and a cylinder stand on equal bases and have the same height.The ratio of their volumes is}\left(a\right)1:2:3\left(b\right)2:1:3\left(c\right)2:3:1\left(d\right)3:2:1$

Answer 1

Volume of cone = ($\frac{1}{3}$)πr²h
Volume of hemisphere = ($\frac{2}{3}$)πr³
Volume of cylinder = πr²h
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 = ($\frac{1}{3}$)πr²h : ($\frac{2}{3}$)πr³ : πr²h
= ($\frac{1}{3}$​​​​​​​)πr³ : ($\frac{2}{3}$​​​​​​​)πr³ : πr³
= ($\frac{1}{3}$) : ($\frac{2}{3}$) : 1
= 1: 2: 3

Ans-a