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 ( square )
check answer remaining attempts : 3

Explanation:

Step1: Recall the volume ratio formula for similar solids

For two similar solids, if the scale factor is \(k\) (small to large), the ratio of their volumes \(V_s/V_l=k^{3}\), where \(V_s\) is the volume of the small solid and \(V_l\) is the volume of the large solid. Here, \(V_s = 64\pi\) and \(V_l=512\pi\). Then \(\frac{V_s}{V_l}=\frac{64\pi}{512\pi}\).
Simplify \(\frac{64\pi}{512\pi}=\frac{64}{512}=\frac{1}{8}\).

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

Since \(\frac{V_s}{V_l}=k^{3}\), and \(\frac{V_s}{V_l}=\frac{1}{8}\), then \(k^{3}=\frac{1}{8}\).
Take the cube - root of both sides: \(k=\sqrt[3]{\frac{1}{8}}\).
We know that \(\sqrt[3]{\frac{1}{8}}=\frac{\sqrt[3]{1}}{\sqrt[3]{8}}\) (using the property \(\sqrt[3]{\frac{a}{b}}=\frac{\sqrt[3]{a}}{\sqrt[3]{b}},b
eq0\)). Since \(\sqrt[3]{1} = 1\) and \(\sqrt[3]{8}=2\), \(k=\frac{1}{2}\).

Answer:

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