Question

Note Take $\mathrm{\pi }=\frac{22}{7}$, unless stated otherwise.
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 moon and earth be r units and R units, respectively.

∴ 2r = $\frac{1}{4}$ × 2R (Given)

⇒ $r=\frac{R}{4}$ .....(1)

$\therefore \frac{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{moon}}{\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{earth}}=\frac{{\displaystyle \frac{4}{3}\mathrm{\pi }{r}^3}}{{\displaystyle \frac{4}{3}\mathrm{\pi }{R}^3}}=\frac{{\displaystyle {\left({\displaystyle \frac{R}{4}}\right)}^3}}{R^3}=\frac{{\displaystyle 1}}{64}$ [Using (1)]

Thus, the volume of the moon is $\frac{1}{64}$ of the volume of the earth.