Question

1. The diameter of the moon is approximately one fourth of the diameter of the earth.
Find the ratio of their surface areas.
​

Answer 1

Answer:

Step-by-step explanation:

The shape of moon and earth is sphere.

Surface Area of sphere is 4$\pi r^{2}$

Let Diameter of Earth = D and Radius = R

Diameter of Moon = d and Radius =r

Given in question, the diameter of the moon is = 1/4 (diameter of Earth)

⇒ d = $\frac{1}{4}$ × D

⇒ $\frac{r}{2}$ = $\frac{1}{4}$ × $\frac{R}{2}$

⇒ r = $\frac{1}{4}$ × $\frac{R}{2}$ ×2

⇒ r = $\frac{R}{4}$.   (let it be equation - 1)

Surface area of Earth = 4$\pi R^{2}$

Surface area of Moon = 4$\pi r^{2}$

Taking the ratio of their surface areas = $\frac{Surface area of Earth}{Surface area of Moon}$

                                         = $\frac{4\pi R^{2}}{4\pi r^{2} }$ = $\frac{R^{2} }{r^{2} }$

                                         = $(\frac{R}{r}) ^{2}$

                                         = $(\frac{R}{\frac{R}{4} })^{2}$           ( From Equation - 1)

                                         =$(\frac{1}{\frac{1}{4} } )^{2}$

                                         = $(\frac{4}{1}) ^{2}$

                                         = $\frac{16}{1}$

∴ Ratio of surface areas of Earth to Moon is 16 : 1