The diameter of the moon is approximately one | vedclass

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Question

(C) Let the radius of the earth be $R$.Since the diameter of the moon is one-fourth of the diameter of the earth,the radius of the moon will also be o

Vedclass · Accepted Answer

$1:16$

Vedclass · Answer

(C) Let the radius of the earth be $R$.Since the diameter of the moon is one-fourth of the diameter of the earth,the radius of the moon will also be one-fourth of the radius of the earth.Therefore,the radius of the moon $= \frac{R}{4}$.The surface area of a sphere is given by the formula $A = 4 \pi r^2$.Surface area of the earth $= 4 \pi R^2$.Surface area of the moon $= 4 \pi \left( \frac{R}{4} ight)^2 = 4 \pi \left( \frac{R^2}{16} ight) = \frac{\pi R^2}{4}$.The ratio of the surface area of the moon to the surface area of the earth is:$\frac{	ext{Surface area of the moon}}{	ext{Surface area of the earth}} = \frac{\frac{\pi R^2}{4}}{4 \pi R^2} = \frac{1}{4 	imes 4} = \frac{1}{16}$.Thus,the ratio of their surface areas is $1:16$.

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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