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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?

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12

23

164

143

answer is C.

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Detailed Solution

Given, the diameter of the moon is approximately one-fourth of the diameter of the earth.
Let the diameter of the earth be x.
Therefore, diameter of the moon is

x 4

.
So, radius of the earth is

x 2

and radius of the moon is

x 8

.
Volume of the sphere is

43 π r 3

.
Volume of the earth,

⇒ 43 π x 2 3

⇒ 43 π × x 3 8

⇒ π x 3 6

Volume of the moon,

⇒ 43 π × x 8 3

⇒ 43 π × x 3 512

⇒ π x 3 384

Their ratio is,

V o l u m e of the moon V o l u m e of the earth = π x 3 384 π x 3 6

⇒ 6384

⇒ 164

Thus, volume of the moon is

164

times of the volume of the earth.
Therefore, the correct option is 3.

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