Question

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

Answer 1

Let the diameter of earth be ${}^{\prime }{d}^{\prime }$. Therefore, the diameter of moon will be $\frac{d}{4}$.

Diameter of moon $=\frac{1}{4}\times$ diameter of earth $=\frac{1}{4}\times d=\frac{d}{4}$ [Given]

Radius of earth $=\frac{d}{2}$

Radius of moon $=\frac{1}{2}\times \frac{d}{4}=\frac{d}{8}$

Surface area of moon $=4\pi (\frac{d}{8}{)}^2$ [$\because$ Surface area of spherical shape object $=4\pi r^2$]

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

Required ratio (Surface area of moon: Surface area of earth) $=\frac{4\pi (\frac{d}{8}{)}^2}{4\pi (\frac{d}{2}{)}^2}$

$=\frac{\frac{d^2}{64}}{\frac{d^2}{4}}=\frac{4}{64}=\frac{1}{16}$

Therefore, the ratio between their surface areas will be $1:16.$