Question

A right cylinder a right cone and a hemisphere have the same height and the same base area then the ratio of their volumes is

• A. 2 : 1 : 4
• B. 1 : 2 : 3
• C. 3 : 1 : 2
• D. 1 : 3. : 2

Answer 1

The correct option is C 3 : 1 : 2

Let radius and height of each of the shapes be $=a$

Required ratio $=Volumeofcylinder:VolumeofCone:Volumeofhemisphere$
$=\pi r^{2}h:\frac{1}{3}\pi r^{2}h:\frac{2}{3}\pi r^3$
$=a^{2}a:\frac{1}{3}{a}^{2}a:\frac{2}{3}{a}^3$
$=a^3:\frac{1}{3}{a}^3:\frac{2}{3}{a}^3$

$ = 1 :\frac{ 1 }{ 3 } :\frac{ 2 }{ 3 } $

$=3:1:2$