Answer:
Option A: [tex]\frac{1}{27}[/tex]
Step-by-step 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:
[tex]radius\ scale\ factor=\frac{6.2}{18.6}\\\\radius\ scale\ factor=\frac{1}{3}[/tex]
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:
[tex]volume\ scale\ factor=(radius\ scale\ factor)^3[/tex]
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: [tex]volume\ scale\ factor=(\frac{1}{3})^3\\\\volume\ scale\ factor=\frac{1}{3}*\frac{1}{3}*\frac{1}{3}\\\\volume\ scale\ factor=\frac{1}{27}[/tex]
Then, the volume of the small sphere is [tex]\frac{1}{27}[/tex] times the volume of the large sphere.
