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Q.

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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a

1 2  

b

2 3  

c

1 64  

d

1 43   

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 4 3 π r 3  .
Volume of the earth,
⇒ 4 3 π x 2 3    ⇒ 4 3 π× x 3 8    ⇒ π x 3 6   Volume of the moon,
⇒ 4 3 π× x 8 3    ⇒ 4 3 π× x 3 512    ⇒ π x 3 384  
Their ratio is,
Volume of the moon Volume of the earth = π x 3 384 π x 3 6    ⇒ 6 384    ⇒ 1 64  
Thus, volume of the moon is 1 64   times of the volume of the earth.
Therefore, the correct option is 3.
 
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