Question

A. 1/27 B. 1/18 C. 1/9 D. 1/3

Answer 1

Answer:

Option A: $\frac{1}{27}$

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:

$radius\ scale\ factor=\frac{6.2}{18.6}\\\\radius\ scale\ factor=\frac{1}{3}$

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:    $volume\ scale\ factor=(\frac{1}{3})^3\\\\volume\ scale\ factor=\frac{1}{3}*\frac{1}{3}*\frac{1}{3}\\\\volume\ scale\ factor=\frac{1}{27}$

Then, the volume of the small sphere is $\frac{1}{27}$ times the volume of the large sphere.