Question

Question 4
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.
Therefore, the radius of the earth will be will be $\frac{d}{2}$.
Diameter of moon will be $\frac{d}{4}$ and the radius of moon will be $\frac{d}{8}$.
Volume of the moon $=\frac{4}{3}\pi r^3=\frac{4}{3}\pi {\left(\frac{d}{8}\right)}^3=\frac{1}{512}\times \frac{4}{3}\pi d^3$
Volume of the earth = $\frac{4}{3}\pi r^3=\frac{4}{3}\pi {\left(\frac{d}{2}\right)}^3=\frac{1}{8}\times \frac{4}{3}\pi d^3$
$\frac{Volumeofmoon}{Volumeofearth}=\frac{\frac{1}{512}\times \frac{4}{3}\pi d^3}{\frac{1}{8}\times \frac{4}{3}\pi d^3}$
$=\frac{1}{64}$
$\Rightarrow$ Volume of the moon $=\frac{1}{64}$ Volume of earth