Question

similar figures and volume practice
complete this assessment to review what youve learned. it will not count toward your grade.
two similar cylinders have volumes of ( 512pi \text{ in.}^3 ), ( 64pi \text{ in.}^3 ), and ( 64pi \text{ in.}^3 ), ( 512pi \text{ in.}^3 ). by comparing volume, what is the scale factor
of the small cylinder to the larger cylinder? (1 point)
the scale factor of the small cylinder to the larger cylinder is
check answer remain

Explanation:

Step1: Recall the volume ratio formula for similar solids

For two similar solids, if the scale factor of the side lengths is \(k\) (small to large), then the ratio of their volumes \(V_1\) (small) and \(V_2\) (large) is \(V_1/V_2=k^{3}\). Here, \(V_1 = 64\pi\) and \(V_2=512\pi\). So, \(\frac{V_1}{V_2}=\frac{64\pi}{512\pi}\).
Simplify \(\frac{64\pi}{512\pi}\) to \(\frac{64}{512}=\frac{1}{8}\).

Step2: Solve for the scale factor \(k\)

Since \(\frac{V_1}{V_2}=k^{3}\), and \(\frac{V_1}{V_2}=\frac{1}{8}\), then \(k^{3}=\frac{1}{8}\).
Take the cube - root of both sides: \(k=\sqrt[3]{\frac{1}{8}}\).
We know that \(\sqrt[3]{\frac{1}{8}}=\frac{1}{2}\) because \((\frac{1}{2})^{3}=\frac{1}{8}\).

Answer:

\(\frac{1}{2}\)