Okay, here we have this:
Considering the provided information we obtain the following:
Let us take the diameter of the earth as d, so the diameter of the moon is d/4
Thus, the earth radius is d/2, and the moon radius is d/4/2=d/8.
Now, let's find the volume of the the earth and the moon separately to finally compare them:
[tex]\begin{gathered} \text{Volume of earth=}\frac{4}{3}\pi r^3 \\ =\frac{4}{3}\pi(\frac{d}{2})^3 \\ =\frac{1}{8}\cdot\frac{4}{3}\pi d^3 \\ =\frac{1}{6}\pi d^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Volume of moon=}\frac{4}{3}\pi r^3 \\ =\frac{4}{3}\pi(\frac{d}{8})^3 \\ =\frac{1}{512}\cdot\frac{4}{3}\pi d^3 \\ =\frac{1}{384}\pi d^3 \end{gathered}[/tex]Finally let's compare its volumes:
[tex]\begin{gathered} \frac{Volume\text{ of moon}}{Volume\text{ of earth}}=\frac{\frac{1}{384}\pi d^3}{\frac{1}{6}\pi d^3} \\ =\frac{1}{64} \end{gathered}[/tex]Finally we obtain that the volume of the moon is 1/64 of the volume of the earth.