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Maths-

General

Easy

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?

The correct answer is: 1/64

Explanation:

We have given the diameter of moon is approximately one fourth of the diameter of the earth.

We have to find the fraction of the volume of the earth is the volume of the moon

Step 1 of 1:
Let the diameter of moon be ,Then the diameter of earth will be 4d
So, Radius of moon will be $d over 2$ . And the radius of earth will be $fraction numerator 4 d over denominator 2 end fraction equals 2 d$
Since, both earth and moon are sphere
We can use formula of volume of sphere $4 over 3 pi r cubed$ .
$V subscript m equals 4 over 3 pi r cubed$
$equals 4 over 3 pi open parentheses d over 2 close parentheses cubed$
$equals fraction numerator pi d cubed over denominator 6 end fraction$
And volume of earth will be
$V subscript E equals 4 over 3 pi r cubed$
$equals 4 over 3 pi left parenthesis 2 d right parenthesis cubed$
$equals fraction numerator 32 pi d cubed over denominator 3 end fraction$
Therefore, the fraction will be
$V subscript m over V subscript E equals fraction numerator pi d cubed divided by 6 over denominator 32 pi d cubed divided by 3 end fraction$
$equals 1 over 64$

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