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 radius of the earth be R and the radius of the moon be r
Diameter of the moon = $\frac{1}{4}$ × diameter of the earth
The radius of the moon = $\frac{1}{4}$ × radius of the earth
r = $\frac{1}{4}$ × R

r = $\frac{R}{4}$

The volume of the earth = $\frac{4}{3}\pi$ R3

The volume of the moon = $\frac{4}{3}\pi$ r3
= $\frac{4}{3}\pi$ $(\frac{R}{4})^3$

= \frac{1}{64} ×\frac{ 4}{3}$$\pi R3

$⇒$ The volume of the moon = $\frac{1}{64}$× Volume of the earth
Therefore, the volume of the moon is $\frac{1}{64}$ times the volume of the earth.