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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?

Given:

The diameter of the moon is approximately one fourth of the diameter of the earth.

To do:

We have to find what fraction of the volume of the earth is the volume of the moon.

Solution:

Diameter of the moon $=\frac{1}{4}$ of the diameter of the earth

Let the diameter of the moon be $2 r$.

This implies,

Radius of the moon $=r$

Radius of earth $(R)=4 r$

Therefore,

Volume of the moon $=\frac{4}{3} \pi r^{3}$

Volume of the earth $=\frac{4}{3} \pi R^{3}$

$=\frac{4}{3} \pi(4 r)^{3}$

$=64 \times \frac{4}{3} \pi r^{3}$

$=64(\frac{4}{3} \pi r^{3})$

$=64 \times$ Volume of the moon

Therefore,

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

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