# What is the Ratio of the Volume of a Cube to that of a Sphere Which Will Fit Inside It? - Mathematics

What is the ratio of the volume of a cube to that of a sphere which will fit inside it?

#### Solution

Ratio of sphere

=1/2 xx "side of cube"

r = a/2

Now,

Volume of cube v_1 = a^3

Volume of sphere

v_2 = 4/3 pir^3

=4/3 pi(a/2)^3

=4/3 pi a^3 / 8

v_2 = 1/6pia^3

The ratio of their volumes

v_1 :v_2 = a^3 :1/6 pia^3

v_1 /v_2 = a^3/(1/6 pia^3)

=6/pi

Hence, v_1 :v_2 = 6 : pi

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Q 10 | Page 87