Question

The diameter of the moon is approximately one fourth of the diameter of the earth.

Find the ratio of their surface areas

Answer 1

Explanation:

Area of a sphere is
`4\pi d^(2)`

let d be the diameter of the moon and D be the diameter of the earth

d = 1/4 D

Area of Earth =
`4\pi D^(2) = 4\pi ((d)/(4) )^(2) = 4\pi (d^(2) )/(16) = \pi (d^(2) )/(4)`

Area of moon =
`4\pi d^(2)`

`(Area of moon)/(Area of Earth) = (1)/(16)`