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.