Chapter 6.4, Problem 36PPS

To determine

To Find:

The scale factor if the old volume was 0.8 cubic feet and the new volume is 21.6 cubic feet.

Answer to Problem 36PPS

3

Explanation of Solution

Given Information:

An online book store wants to increase the size of the boxes it uses to ship orders. The new volume N is equal to the old volume V times the scale factor F cubed, or

  $N=V\cdot F^3$

Calculation:

• Given

  $N=V\cdot F^3$

And

V=0.8

N=21.6

• Substituting the above values in the equation to find F:

  $\begin{array}{l}N=V\cdot F^3\\ and\\ \begin{array}{l}V=0.8\hfill \\ N=21.6\hfill \end{array}\\ \Rightarrow 21.6=0.8\times F^3\\ \Rightarrow F^3=\frac{21.6}{0.8}\mathrm{...................}[divide"0.8"each\_side]\\ \Rightarrow F=\sqrt[3]{\frac{21.6}{0.8}}=\sqrt[3]{27}=3\end{array}$

So, the scale factor is 3.