# The function of the height of the closed rectangular box in terms of the width and its domain.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

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.

Expert Solution

The formula for the height of the closed rectangular box as a function of the width is h(w)=4w2 .

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×b×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=2w2h .

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

8=2w2hh=82w2=4w2

The formula for the height of the closed rectangular box as a function of the width is h(w)=4w2 .

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

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