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# 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 :

Let the diameter of earth be d.
Therefore, the diameter of moon will be $$\frac{d}{4}$$.
Thus, Radius of earth = $$\frac{d}{2}$$
$$\therefore$$ Radius of moon
= $$\frac{1}{2}$$ × $$\frac{d}{4}$$
= $$\frac{d}{8}$$

Now, Volume of moon
= $$\frac{4}{3}{\pi}{r}^3$$
= $$\frac{4}{3}{\pi} × {\frac{d}{8}}^3$$
=$$\frac{1}{512} × \frac{4}{3}{\pi} × {d}^3$$

Similarly,
Volume of earth
= $$\frac{4}{3}{\pi}{r}^3$$
=$$\frac{4}{3}{\pi} × {\frac{d}{2}}^3$$
= $$\frac{1}{8} × \frac{4}{3}{\pi} × {d}^3$$

$$\therefore$$ $$\frac{Volume of moon}{Volume of earth}$$
=$$\frac{\frac{1}{512} × \frac{4}{3}{\pi} × {d}^3}{\frac{1}{8} × \frac{4}{3}{\pi} × {d}^3}$$
= $$\frac{1}{64}$$

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