Similar Figures and Volume Practice Complete this assessment to review what you’ve learned. It will not count toward your grade. 3 of 53 of 5 Items Question Two similar cylinders have volumes of 512π in.3 and 64π in.3 . By comparing volume, what is the scale factor of the small cylinder to the larger cylinder?(1 point) Remaining Attempts : 3 Skip to navigation page 13 of 14 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To find the scale factor of the small cylinder to the larger cylinder using their volumes, we can use the following relationship between the volumes of similar figures. If two similar figures have a scale factor of \( k \), then the ratio of their volumes is given by \( k^3 \).

Given volumes:

• Volume of the larger cylinder: \( 512\pi \) in³
• Volume of the smaller cylinder: \( 64\pi \) in³

First, find the ratio of the volumes:

\[ \text{Ratio} = \frac{\text{Volume of small cylinder}}{\text{Volume of larger cylinder}} = \frac{64\pi}{512\pi} \]

The \(\pi\) cancels out:

\[ \text{Ratio} = \frac{64}{512} = \frac{1}{8} \]

Now, if \( k \) is the scale factor from the small cylinder to the larger cylinder, then:

\[ k^3 = \frac{1}{8} \]

To find \( k \), we take the cube root of both sides:

\[ k = \sqrt[3]{\frac{1}{8}} = \frac{1}{2} \]

Therefore, the scale factor of the small cylinder to the larger cylinder is \( \frac{1}{2} \).