Question

The diameter of the moon is approximately one
fourth of the diameter of the earth. Find the
ratio of their surface areas
a) 1:4 b) 1:16 c) 1:2 do 16​

Answer 1

Answer:

The answer is A) 1:16.

Step-by-step explanation:

Let the radius of earth = r

=>Radius of moon = r/4

=>Surface area of sphere = 4πr^2

Since, the Earth as well as the Moon are considered to be as a spheres.

Surface area of Earth = 4πr^2

The surface area of Moon = 4π(r/4)^2

=> Surface area of the Earth/Surface area of the Moon = 4πr^2 / 4π(r/4)^2 = r^2 / (r/4)^2 = 16r^2 / r^2

Let the radius of earth = r

=>Radius of moon = r/4

=>Surface area of sphere = 4πr^2Since, the Earth as well as the Moon are considered to be as a spheres.

Surface area of Earth = 4πr^2The surface area of Moon = 4π(r/4)^2

=> Surface area of the Earth/Surface area of the Moon = 4πr^2 / 4π(r/4)^2 = r^2 / (r/4)^2 = 16r^2 / r^2 = 16 / 1

OR

[Surface area of the Moon/ Surface area of the Earth] = 1:16

Thus, required ratio = 1:16