Q : 7    The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.
 

Answers (1)

Let diameter of Moon be d_m and diameter of Earth be d_e

We know,

The surface area of a sphere of radius r = 4\pi r^2

\therefore The ratio of their surface areas = \frac{Surface\ area\ of\ moon}{Surface\ area\ of\ Earth}

= \frac{4\pi \left (\frac{d_m}{2} \right )^2}{4\pi \left (\frac{d_e}{2} \right )^2}

= \frac{d_m^2}{d_e^2}

=\left ( \frac{\frac{1}{4}d_e}{d_e} \right )^2

= \frac{1}{16}

Therefore, the ratio of the surface areas of the moon and earth is = 1:16 

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