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.