Question

the diameter of the moon is 1/4 the diameter of the earth. what fraction is the volume of the earth to the volume of the moon.​

Answer 1

Answer:

Therefore, ratio of their volume is 1:64

Step-by-step explanation:

Let radius of Earth be x

Now,the radius of Moon =x/4

We know that,

Volume of Sphere =4/3πr^3

So, Volume of Earth =4/3πx^3

And, Volume of Moon =4/3π (x/4)^3

Now, ratio of their volume=

4/3πx^3 : 4/3π (x/4)^3

x^3 : (x/4)^3

x^3 : x^3/64

1:64

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