Question

Diameter of the earth is four times (approximately) the diameter of the moon, then the ratio of their surface area is :

• A. $4:1$
• B. $8:1$
• C. $16:1$
• D. $64:1$

Answer 1

The correct option is C $16:1$

Let diameter of Earth $=D$ units

$\therefore$ Radius of Earth $=2R$ units

Let diameter of moon $=d$ units

Radius of mood $=2r$ units

Given, $D=4d$

$2R=4\times 2r$

$R=4r$

$\frac{SurfaceareaofEarth}{Surfaceareaofmoon}=\frac{4\pi R^2}{4\pi r^2}=\frac{4\pi {\left(4r\right)}^2}{4\pi r^2}=\frac{64\pi r^2}{4\pi r^2}=\frac{16}{1}$