Chapter 8, Problem 7STP

To determine

From the list which is not the dimension of the box.

Answer to Problem 7STP

The correct option is A.

Explanation of Solution

Given:

The rectangular gift box has the dimensions that can be represented as shown below:

  

The volume of the box is 672 cubic inches.

The options are given as:

  $\begin{array}{l}\text{A}\text{6in}\\ \text{B}7\text{in}\text{.}\\ \text{C 8in}\text{.}\\ \text{D 12in}\text{.}\end{array}$

The volume of the cube is given as:

  $\text{Volume=lengh×width×height}$

Now, put the known values into the above equation:

  $\begin{array}{l}\text{Volume=}w\text{×}\left(w-5\right)\text{×}\left(w-4\right)\\ 672=w^3-4w^2-5w^2+20w\\ w^3-9w^2+20w-652=0\end{array}$

Solving the above equation:

The sides of the cubes will be:

  $\begin{array}{c}w-4=12-4\\ =8\text{in}\text{.}\\ w-5=12-5\\ =7\text{in}.\\ w=12\text{in}.\end{array}$

Therefore, the correct option is A.