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 moon .​

Answer 1

Let,

D be the diameter of earth.

R be the radius of earth.

d be the diameter of moon.

r be the radius of moon.

A/Q,

d = ¼D

(since diameter = 2×radius)

So, above eqn. becomes,

(2r) = ¼(2R)

=> r = ¼ R -----(i)

Now,

Volume of earth = (4/3)×π×R³ ----(ii)

Volume of moon = (4/3)×π×r³

= (4/3)×π×(¼R)³ {from (i)}

= (4/3)×π×(1/64)R³

= 1/64 { (4/3)×π×R³}

Now, using eqn. (ii) in above eqn.

we have,

Volume of moon = 1/64 Volume of earth

Therefore 1/64 fraction of volume of earth is the volume of moon.