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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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