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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.
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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