Question.
The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.
Solution:
Let the diameter of earth be $d$. Therefore, the diameter of moon will be $\frac{d}{4}$.
Radius of earth $=\frac{d}{2}$
Radius of moon $=\frac{1}{2} \times \frac{d}{4}=\frac{d}{8}$
Surface area of moon $=4 \pi\left(\frac{d}{8}\right)^{2}$
Surface area of earth $=4 \pi\left(\frac{d}{2}\right)^{2}$
Required ratio $=\frac{4 \pi\left(\frac{d}{8}\right)^{2}}{4 \pi\left(\frac{d}{2}\right)^{2}}$
$=\frac{4}{64}=\frac{1}{16}$
Therefore, the ratio between their surface areas will be 1:16.
Let the diameter of earth be $d$. Therefore, the diameter of moon will be $\frac{d}{4}$.
Radius of earth $=\frac{d}{2}$
Radius of moon $=\frac{1}{2} \times \frac{d}{4}=\frac{d}{8}$
Surface area of moon $=4 \pi\left(\frac{d}{8}\right)^{2}$
Surface area of earth $=4 \pi\left(\frac{d}{2}\right)^{2}$
Required ratio $=\frac{4 \pi\left(\frac{d}{8}\right)^{2}}{4 \pi\left(\frac{d}{2}\right)^{2}}$
$=\frac{4}{64}=\frac{1}{16}$
Therefore, the ratio between their surface areas will be 1:16.