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?

Answer 1

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

The diameter of the moon will be `d/4`, and the radius of the moon will be `d/8`.

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

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

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

⇒ Volume of the moon = `1/64  "Volume of the earth"`

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