Question

A cylinder, a cone and a hemisphere have bases of equal radii and are of equal heights. Then the ratio of their volumes is ………

A) 3 : 1 : 2 

B) 3 : 2 :1 

C) 1 : 2 : 3 

D) 1 : 3 : 2

Answer 1

Correct option is: A) 3 : 1 : 2

Let r be the radii of cylinder, cone & hemisphere.

\(\because\) Height of hemisphere = Radius of hemisphere = r

\(\therefore\) Height of cone = Height of cylinder = r

\(\therefore\) h = r

Now, volume of cylinder : Volume of cone ; Volume of hemisphere.

= \(\pi r^2h : \frac 13 \pi r^2h : \frac 23 \pi r^3\)

= 3h : h : 2r (On dividing by \(\frac {\pi r^2}{3}\))

= 3r : r : 2r (\(\because\) h = r)

= 3 : 1 : 2 (On dividing by r)

Hence, the ratio of their volumes is 3 : 1 : 2.

Answer 2

Correct option is: A) 3 : 1 : 2