Question

Find the fraction of volume of earth to volume of moon , if the diameter of moon is approximately 1/4th of earth.

Answer 1

Diameter = d
Radius = r

let d of earth = A
so,
d of moon will be = A/4

from now
r of earth = A/2
and
r of moon = 1/2 * A/4 = A/8

now
from the formula ( see picture above)

= (A/8)^3 / ( A/2)^3

= A^3/8^3 / A^3/2^3

=A^3/8^3 * 2^3/A^3
now,
A^3 will cancel out by A^3

then
= 2^3/8^3
=2*2*2 / 8*8*8
= 1 /4*4*4
1/64

so,
volume of moon = 1/64 ( volume of earth)

hence,the volume of earth is 1/64 of the volume of the 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