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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 areas.
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Solution
Let the diameter of the earth is d then, diameter of moon will be `d/4`
Radius of earth =`d/2`
Radius of moon = `2/4=d/8`
S.A of moon = `4πr(d/8)^2`
Surface area of earth = `4πr(d/2)^2`
Required ratio = `(4πr(d/8)^2)/(4πr(d/2)^2) = 4/64=1/16`
Thus, the required ratio of the surface areas is `1/16`.
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