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Question
The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.
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Solution
Let the diameter of earth be d. Therefore, the diameter of the moon will be `d/4`.
Radius of earth = `d/2`
Radius of moon = `1/2xxd/4 = d/8`
Surface area of moon = `4pi(d/8)^2`
Surface area of earth = `4pi(d/2)^2`
Required ratio = `(4pi(d/8)^2)/(4pi(d/2)^2)=4/64=1/16`
Therefore, the ratio between their surface areas will be 1 : 16.
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