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 the Moon

Answer 1

d(e) of earth = x , radius (r) of earth = x/2

d(m) of moon = x/4 , radius of moon = x/4*2 = x/8

volume of earth = 4/3πr^3

= 4/3π* x/2*x/2*x/2

= 4/3πx^3/8

vol of moon = 4/3π*(x/8)^3

= 4/3π*x^3/512

vol of moon / vol of earth

now refer the attacment

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