Start your trial now! First week only $4.99!*arrow_forward*

BuyFind*launch*

4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.1, Problem 57E

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.

Expert Solution

The formula for the surface area of the open rectangular box as a function of the length of a side of the base is

The domain of the surface area of the open rectangular box as a function of the length of a side of the base is

**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

That is,

Substitute the value of *h* in

Therefore, the formula for the surface area (*S*) of the open rectangular box as a function of the length of a side of the base (*a*) is

The domain of the surface area of the open rectangular box as a function of the length of a side of the base is