Chapter 1.1, Problem 56E

To determine

To find: The function of the height of the closed rectangular box in terms of the width and its domain.

Answer to Problem 56E

The formula for the height of the closed rectangular box as a function of the width is $h\left(w\right)=\frac{4}{w^2}$.

The domain of the function of the height of the closed rectangular box in terms of width is $w>0$.

Explanation of Solution

Given:

The volume of the closed rectangular box is 8 ft³. The length of the rectangular box is twice its width.

Formula used:

Volume of the rectangular box of length l, width b, height h is $V=l\times b\times h$.

Calculation:

Let the width of the rectangular box be w. Then, the length of the rectangular box is 2w.

And, the height of the rectangular box is h.

Thus, the volume of the rectangular box is, $V=2w^{2}h$.

Since the volume of the closed rectangular box is 8ft³, the height of the rectangular box is computed as follows:

$\begin{array}{c}8=2w^{2}h\\ h=\frac{8}{2w^2}\\ =\frac{4}{w^2}\end{array}$

The formula for the height of the closed rectangular box as a function of the width is $h\left(w\right)=\frac{4}{w^2}$.

The domain of the function of the height of the closed rectangular box in terms of width is $w>0$.