Question

the diameter of the moon is apparently one. fourth of the daimeter of the earth what fraction of the volume of the earth is the volume of the moon

Answer 1

$let \: re = x \\ rm = \frac{1}{4}x \\ \frac{ve}{vm} = \frac{ \frac{4}{3}\pi {(re)}^{3} }{ \frac{4}{3}\pi {(rm)}^{3} } = {( \frac{re}{rm} )}^{3} = {( \frac{x}{ \frac{1}{4} x}) }^{3} = \frac{64}{1}$

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