Question

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

Answer 1

let diameter of moon be x
therefore,radius=x/2
surface area=4πr^2
4π(x/2)^2=4πx^2/4
=πx^2

diameter of earth=4x
therefore,r=4x/2
=2x
surface area=4πr^2
=16πx^2

the ratio of their surface area=16πx^2/πx^2
=16/1
=16:1
....

Answer 2

Hey there!

$\text{Let the diameter of Earth be d}\\\text{Moon's diameter} =\frac{x}{4}\\\text{Radius of earth = r}= \frac{x}{2}\\\text{Radius of Moon = R} = \frac{x}{8}\\\\\text{Ratio of T.S.A} = \frac{\text{Surface area of moon}}{\text{Surface area of earth}}\\~~~~~~~~~~~~~~~~~~~~=\frac{4\pi R^2}{4\pi r^2}\\~~~~~~~~~~~~~~~~~~~~=\frac{(\frac{x}{8})^2}{(\frac{x}{2})^2}\\~~~~~~~~~~~~~~~~~~~~=\frac{1}{16}\\\\\boxed{\boxed{\bold{Ratio = 1:16}}}$