The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

 Given:

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

To do:

We have to find the ratio of their surface areas.

Solution:

Diameter of the moon $=\frac{1}{4}$ of diameter of the earth

Let the radius of the earth be $r$ km.

This implies,

Radius of the moon $=\frac{1}{4}r$ km

Therefore,

Surface area of the earth $= 4\pi r^2$

Surface area of the moon $=4 \pi(\frac{1}{4} r)^{2}$

$=4 \pi \times \frac{1}{16} r^{2}$

$=\frac{1}{4} \pi r^{2}$

Ratio of the surface area of the moon and the earth $=\frac{1}{4} \pi r^{2}: 4 \pi r^{2}$

$=\frac{1}{4}: 4$

$=1: 16$

The ratio of their surface areas is $1:16$.

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Updated on: 10-Oct-2022

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