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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 moon will be d4.

Diameter of moon =14× diameter of earth =14×d=d4 [Given]

Radius of earth =d2

Radius of moon =12×d4=d8

Surface area of moon =4π(d8)2 [ Surface area of spherical shape object =4πr2]

Surface area of earth =4π(d2)2

Required ratio (Surface area of moon: Surface area of earth) =4π(d8)24π(d2)2

=d264d24=464=116

Therefore, the ratio between their surface areas will be 1:16.


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