Question

Suppose planet A's diameter is approximately 8 times planet B's and both bodies are spheres. What is the ratio of their volumes?

Answer 1

Answer:

The ratio of planet B's volume to planet A's volume is 1:512 or 1/512

Step-by-step explanation:

Volume of sphere = 4/3 π r^3

r = d/2

Radius of palnet A = 8/2 = 4

Radius of planet B = 1/2

Since 4/3 π is same in both volumes so, they cancel out when finding ratio.

Now ratio depends on radius cube of both planets

Volume of Planet B : Volume of Planet A

4/3 π(1/2)^3 :  4/3 π(4)^3

Cancelling  4/3 π on both sides

1/8 : 64

Multiply 8 on both sides

1 : 512

So, The ratio of planet B's volume to planet A's volume is 1:512 or 1/512