The diameter of the moon is approximately 1/4th of the Earth. What will be the ratio of their volumes? v = (4)/(3)\pi {r}^(2) ​

Question

The diameter of the moon is approximately 1/4th of the Earth. What will be the ratio of their volumes?


`v = (4)/(3)\pi {r}^(2)`
​

Answer 1

Let A and B be two spheres with radii
`r_A[tex] and [tex]r_B`, respectively. The ratio between their volumes is

`((4)/(3)\pi r_A^3)/((4)/(3)\pi r_B^3)=(r_A^3)/(r_B^3)=\left((r_A)/(r_B)\right)^3`

So, the ratio of the volumes of two spheres is the cube of the ratio between the radii.

Since the two radii are in ratio 1:4, the two volumes will be in ratio 1:64, since 4^3=64.

So, the volume of the Earth is about 64 times the volume of the Moon.