Question

the diameter of the moon is approximately ome fourth of the diameter of the earth. what fraction of the volume of the earth is the volume of the moon

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 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