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

Consider d as the diameter of the earth

So radius of the earth = d/2

Consider d/4 as the diameter of the moon

So radius of the moon = d/8

We know that

Volume of moon = 4/3 π (d/8)³

On further calculation

Volume of moon = 1/512 × 4/3 πd³

We know that

Volume of earth = 4/3 π (d/2)³

On further calculation

Volume of earth = 1/8 × 4/3 πd³

So we get

Volume of moon/ Volume of earth = (1/512 × 4/3 πd³)/ (1/8 × 4/3 πd³)

On further calculation

Volume of moon/ Volume of earth = 1/64

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