MCQ

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

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#### Solution

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 (*V*_{1}) = `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 (*V*_{2}) = S^{3}

= x^{3}

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****.**

Concept: Surface Area of a Sphere

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