Question

A sphere and a cube are of the same height. The ratio of their volumes is 

Options

• 3 : 4

•  21 : 11

• 4 : 3

• 11 : 21

Answer 1

In the given problem, we have a sphere and a cube of equal heights. So, let the diameter of the sphere and side of the cube be x units.

So, volume of the sphere (V₁) = `4/3 pi (d/2)^3`

`=4/3 pi (x/2)^3`

`=4/3 pi (x^3 /8)`

`= (pi x^3)/6`

Volume of the cube (V₂) = S³

= x³

So, to find the ratio of the volumes,

`V_1/V-2 = (pi x^3/6)/x^3`

            ` = pi /6` 

           ` = ((22/7))/6`

           `=11/21 `

Therefore, the ratio of the volumes of sphere and cube of equal heights is  11 : 21.