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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?

Q : 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?
 

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Given,

Let d_e be the diameters of Earth

\therefore The diameter of the Moon = d_m = \frac{1}{4}d_e

We know, Volume of a sphere =

 \frac{4}{3}\pi r^3 =\frac{4}{3}\pi \left (\frac{d}{2} \right )^3 = \frac{1}{6}\pi d^3

\therefore The ratio of the volumes = \frac{Volume\ of\ the\ Earth}{Volume\ of\ the\ Moon}

\\ = \frac{\frac{1}{6}\pi d_e^3}{\frac{1}{6}\pi d_m^3} \\ = \frac{ d_e^3}{(\frac{d_e}{4})^3} \\ = 64: 1

Therefore, the required ratio of the volume of the moon to the  volume of the earth is 1: 64

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