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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