Question

The diameter of the moon is approximately one fourth of the diameter of the earth. find the ratio of there surface area? ​

Answer 1

Answer:

Refers to the attachment

Answer 2

ANSWER -

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