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

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 (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. 

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 21 Surface Areas and Volume of a Sphere
Q 4 | Page 25
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