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 metre. Then diameter of moon is $\frac{d}{4}$ metre.

$V_1$ = Volume of earth = $\frac{4}{3}\pi (\frac{d}{2}{)}^3$ $m^3$ = $\frac{\pi }{6}{d}^3$ $m^3$

$V_2$ = Volume of moon = $\frac{4}{3}\pi (\frac{d}{8}{)}^3$ $m^3$ = $\frac{\pi }{384}{d}^3$ $m^3$

Therefore,

$\frac{V_1}{V_2}=\frac{1}{64}$