Chapter 1.1, Problem 61E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

Find a formula for the described function and state its domain.

**61.** An open rectangular box with volume 2 m^{3} has a square base. Express the surface area of the box as a function of the length of a side of the base.

To determine

**To find:** The function of the surface area of the open rectangular box with a square base in terms of the length of a side of the base and the domain of the function.

Explanation

**Given:**

The volume of the open rectangular box with a square base is 2 m^{3}.

**Formula used:**

Volume of the rectangular box of length *l*, width *b*, height *h* is,

Surface area of the open rectangular box of length *l*, width *b*, height *h* is,

**Calculation**:

Let the length of the open rectangular box be *a* and the height of the open rectangular box is *h*.

Since the base of the open rectangular box is a square, the width of the box is same as the length. Therefore, the width of the open rectangular box is *a.*

Volume of the open rectangular box is,

That is,

Since the volume of the open rectangular box with a square base is 2 m^{3}, the height of the box is computed as follows:

Thus, the surface area of the open rectangular box is

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