Question

The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

Answer 1

we know volume of spherical body directly proportional to cube of their radius.
now use it in this question
let earth radius R
then moon's radius =R/4
now
volume of earth/volume of moon=(radius of earth/radius of moon)^3
={R/(R/4)}^3=64
hence
volume of earth=64 x volume of moon

Answer 2

⇒ Let the diameter of the earth be d metre.

⇒ And, the diameter of moon is d/4 metre.

⇒ V1 = Volume of earth

⇒ V2 = Volume of moon

⇒ Volume of sphere = 4/3 π (r^3)

⇒ V1 = 4/3π(d/2)^3

⇒ V1 = π/6(d)^3

⇒ V2 = 4/3π(d/8)^3

⇒ V2 = π/384(d)^3

⇒ V1/V2

⇒ 1/64