Advertisement Remove all ads

# 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

Advertisement Remove all ads

#### 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.

Is there an error in this question or solution?
Advertisement Remove all ads

#### APPEARS IN

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

#### Video TutorialsVIEW ALL 

Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?
Course