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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2: 1

4: 1

16: 1

64: 1

answer is D.

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Detailed Solution

Given that, the diameter of the moon is approximately one-fourth of the diameter of the earth.
Let the radius of the earth be ‘e’ km and the radius of the moon be ‘m’ km.
Given the ratio of radii =

e m = 41

.
The volume of a sphere is given as

43 π r 3

.
The volume of earth will be

V E = 43 π e 3

and the volume of the moon would be

V m = 43 π m 3

.
Now,

⇒ V E V m = 43 π e 3 43 π m 3 = e 3 m 3 = e m 3 Putting the value e m = 41 we get: ⇒ V E V m = 413 = 641

Thus, the ratio of the volume of the earth to the volume of the moon is 64: 1.
Therefore, the correct option is 4.

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