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

• 3 : 4

•  21 : 11

• 4 : 3

• 11 : 21

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