Question

Diameter of moon is approx on fourth of diameter of earth.Find ratio of their surface areas.

Answer 1

Let the diameter of moon be d and earth be D
Given d = (1/4) D
Hence (d/D) = (1/4)
Hence (r/R) = (1/4)
Volume of moon / Volume of earth = (4/3)πr3 /  (4/3)πR3
= r3 / R3
= (r/R)3
= (1/4)3
= 1/64
Hence volume of moon will be (1/64)th volume of earth

Answer 2

Let radius of earth be r so the radius of moon = r/4. (If diameter of moon is one fourth of earth's diameter then the radius would also be one fourth.)

Both are spheres.

Volume of Shpere = 4/3* πr3

Volume of Earth = 4/3* πr3

Volume of Moon = 4/3* π(r/4)3

Their Ratio = 4/3*π(r/4)3 / 4/3*πr3 = 1/64

So 1/64th of the volume of the earth is the volume of the moon.