The diameter of the moon is approximately one-fourth of the diameter of the earth. What is the ratio of their surface areas?

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2: 1

4: 1

8:1

16: 1

answer is D.

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Detailed Solution

Given, the diameter of the moon is approximately one-fourth of the diameter of the earth.
Let the radius of the earth be ‘e’ km and radius of the moon be ‘m’ km.
Given ratio of radii =

e m = 41

.
Surface area of a sphere is given as

V o l u m e = 4 π r 2

.
The surface area of Earth will be

S E = 4 π e 2

and the surface of moon would be

S m = 4 π m 2

.
Now,

S E S m = 4 π e 2 4 π m 2 = e 2 m 2 = e m 2 Putting the value e m = 41, we get: S E S m = 412 = 161

Thus, the ratio of surface area of earth to surface area of moon is 16: 1.
Therefore, the correct option is 4.

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