Question

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

Please answer my questions in detailed.​

Answer 1

Answer:

Required ratio is 16 : 1.

Step-by-step explanation:

Here,

We are considering moon as well as Earth to be an sphere.

Given,

Diameter of moon = 1 / 4 x diameter of the Earth.

= > 2 x radius of moon = 1 / 4 x 2 x radius of the Earth

= > 2 radius of moon = 1 / 2 radius of Earth

= > ( 2 x 2 ) / 1 = radius of Earth / radius of moon

= > 4 : 1 = radius of Earth : radius of moon ...( 1 )

From the properties of spherical objects :

• Surface area of sphere = 4 π r^2 , where r represents the radius of that sphere

We have to find the ratio of surface areas of moon and earth.

Let the radius of moon be r and radius of Earth be R.

= > Surface area of Earth : Surface area of moon

= > 4πR^2 : 4πr^2

= > R^2 : r^2

= > ( R : r )^2

= > ( Radius of Earth : Radius of moon )^2

= > ( 4 : 1 )^2 { from ( 1 ) }

= > 16 : 1

Hence the required ratio is 16 : 1.

Answer 2

$\huge\orange{Hi!}$

Let the diameter of moon be x.

:. Radius of moon=x/2

Diameter of earth =4x

:. Radius of earth =4x/2=2x

Here we are considering moon and earth to be a complete Sphere.

So,

The total surface area(TSA) of sphere =4πr²

Ratio of there TSA:-

$ratio = \frac{tsa \: of \: moon}{tsa \: of \: earth}$

$= > \frac{ 4\pi ({ \frac{x}{2} )}^{2} }{4\pi {(2x)}^{2} }$

$= > \frac{4 \pi (\frac{x}{2} \times \frac{x}{2} ) }{4\pi(2x \times 2x)}$

$= > \frac{ \frac{x}{2} \times \frac{x}{2} }{2x \times 2x}$

$= > \frac{1}{16}$

Ratio=1/16= 1:16

The ratio of the surface areas of moon and earth respectively =1:16

$\huge\red{Follow\:me}$