The diameter of the moon is approximately one-fourth of the diameter of the earth.

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 be d

Then,

Diameter of moon will be d/4

Radius of earth = d/2

Radius of moon $=\frac{\frac{\mathrm{d}}{2}}{4}=\frac{\mathrm{d}}{8}$

Surface area of moon $=4 \pi(\mathrm{d} / 8)^{2}$

Surface area of earth $=4 \pi(d / 2)^{2}$

Required Ratio $=\frac{4 \pi\left(\frac{\mathrm{d}}{8}\right)^{2}}{4 \pi\left(\frac{\mathrm{d}}{2}\right)^{2}}$

$=\frac{4}{64}=\frac{1}{16}$

Thus the required ratio of the surface areas is 1/16

 

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