Question

The diameter of moon is approximately 1 by 4 of the diameter of earth what fraction of volume of earth volume of moon ?

Answer 1

Let the diameter of Earth be x and its radius x/2.

Let the diameter of moon be 1/4x and its radius be 1/8x.

Volume of earth= 4/3×π×(x/2)^3
Volume of moon=4/3×π×(x/8)^3

Ratio of volumes ={4/3×π×(x/8)^3}/{4/3×π×(x/2)^3}
=1/8

Therefore,1/8 of earth' s volume is moon's volume.

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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