Question

Suppose you have two similar rectangular prisms. The volume of the smaller rectangular prism is 64 in^3 and the volume of the larger rectangular prism is 1331 in^3. What is the scale factor of the smaller figure to the larger figure?A) 4:11B) 1:21C) 3:10D) 9:25

Answer 1

Answer:

The scale factor of the smaller figure to the larger figure is 4:11 (option A)

Explanation:

Given:

The volume of the smaller rectangular prism = 64 in^3

The volume of a larger rectangular prism = 1331 in^3

The prisms are similar

To find:

the scale factor of the smaller figure to the larger figure

For similar shapes, the scale factor of the shapes when the volumes are given:

$\frac{Volume\text{ of the smaller figure}}{Volume\text{ of the larger figure}}\text{ = \lparen scale factor\rparen}^3$$\begin{gathered} \frac{64}{1331}\text{ = \lparen scale factor\rparen}^3 \\ \\ cube\text{ root both sides:} \\ \sqrt[3]{\frac{64}{1331}}\text{ = }\sqrt[3]{(scale\text{ factor\rparen}^3} \\ \\ \sqrt[3]{\frac{4^3}{11^3}}\text{ = }\sqrt[3]{(scale\text{ factor\rparen}^3} \\ \\ \frac{4}{11}\text{ = scale factor} \end{gathered}$

The scale factor of the smaller figure to the larger figure is 4:11 (option A)