CPM Homework Help : CCG Problem 10-57

A cylinder with volume $500π\text{ cm}^3$ is similar to a smaller cylinder. If the scale factor is $\frac { 1 } { 5 }$ , what is the volume of the smaller cylinder? Explain your reasoning.

Step 1:

Find the volume scale factor.
$\text{Volume Scale Factor = (Scale Factor)}^3=\left(\frac{1}{3}\right)^3=\frac{1}{125}$

Step 2:

Find the volume of the smaller cylinder.
$500\pi\ \text{cm}^3\left(\frac{1}{125}\right)$

Answer:

$4\pi\text{ cm}^3$