Question

A. 1/27

B. 1/18

C. 1/9

D. 1/3

Answer 1

Option A:
`(1)/(27)`

Explanation:

The first step to solve this exercise is to find the scale factor from the radius of the small sphere to the radius of the large sphere. This is:

`radius\ scale\ factor=(6.2)/(18.6)\\\\radius\ scale\ factor=(1)/(3)`

The second step is to find the scale factor from the volume of the small sphere to the volume of the large sphere. By definition, this will be:

`volume\ scale\ factor=(radius\ scale\ factor)^3`

Therefore, you must substitute the radius scale factor into the equation and then you must evaluate in order to find the volume scale factor. This is:
`volume\ scale\ factor=((1)/(3))^3\\\\volume\ scale\ factor=(1)/(3)*(1)/(3)*(1)/(3)\\\\volume\ scale\ factor=(1)/(27)`

Then, the volume of the small sphere is
`(1)/(27)` times the volume of the large sphere.