Question

A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?

Answer 1

Let the diameter of the base for all three be x cm and height be y cm.

For hemisphere radius  `x /2 cm`

Height `y = x/2 cm`

(As height of the hemisphere is equal to the radius of hemisphere)

For cone

Radius `= x /2 cm`

Height `= x /2 cm`

(As height is same for all)

For cylinder

Radius `= x /2 cm`

Height `= x /2 cm`

The ratio of their volume is

= cylinder volume : conic volume : hemispherical volume

`  = pi (x/2)^2 x /2 :1/3 pi (x/2)^2 (x/2) :2/3 pi (x/3)^3`

`=1 :1/3 :2/3`

`=3:1:2`