Question

the diameter of moon s aproximately onefourthof the earth find ratio of their surfaces area

Answer 1

let Diameter of Earth = D

Diameter of Moon = D / 4

Radius of Earth = D / 2

Radius of Moon = D / 8

Earth and Moon are like spheres.

so Volume 0f Earth = 4 / 3 × π(D/2)^3

and Volume of Moon = 4 / 3 × π (D/8)^3

so ratio of their volumes.

= 512/8 = 64:1

Curved Surface area of Earth = 4π(D/2)^2

Curved Surface area of Moon = 4π(D/8)^2

so ratio of their surface area.

= 64/4 = 16:1