#### Question

The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

#### Solution 1

Let the diameter of earth be *d*. Therefore, the radius of earth will be d/2.

Diameter of moon will be d/4 and the radius of moon will be d/8.

`"Volume of moon "=4/3pir^3=4/3pi(d/8)^3=1/512xx4/3pid^3`

`"Volume of earth "=4/3pi^3=4/3pi(d/2)^3=1/8xx4/3pid^3`

`"Volume of moon"/"Volume of earth"=(1/512xx4/3pid^3)/(1/8xx4/3pid^3)=1/64`

`rArr "Volume of moon "=1/64"Volume of earth"`

Therefore, the volume of moon is **1/64** of the volume of earth.

#### Solution 2

Given that,

The diameter of the moon is approximately one fourth of the diameter of the earth.

Let diameter of earth bed. So radius =`d/2`

Then, diameter of moon`=d/4,radius =2/4=d/8`

Volume of moon `=4/3πr^3=4/3π(d/8)^3=4/3xx1/512πd^3`

Volume of earth `=4/3πr^3=4/3π(d/2)^3=1/8xx4/3πd^3`

`"Volume of moon"/"Volume of earth"=(1/512xx4/3πd^3)/(1/8xx4/3πd^3)=1/64`

Thus, the volume of moon is `1/64`of volume of earth.