### Home > CCG > Chapter 10 > Lesson 10.1.5 > Problem10-57

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.

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

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

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