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Question

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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Solution

Step 1: Find the volume of earth and moon.

Let the diameter of earth =dkm, so the radius (r1)=d2km

Therefore diameter of moon =d4km and radius of moon (r2)=d8km

Volume of the earth =43πr13 [As the volume of sphere =43πr3]

=43πxd22=43πd38..............................(i)

Similarly, Volume of the moon =43πr23

=43πxd82=43πd3512..............................(i)

Step 2: Finding the volume of moon in terms of the volume of the earth.

Volumeofmoonvolumeofearth=43πd351243πd38Volumeofmoonvolumeofearth=164volumeofmoon=164ofvolumeofearth

Hence , the volume of the moon is 164th of the volume of the earth.


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