# What are the dimensions of a box that will use the minimum amount of materials, if the firm needs a closed box in which the bottom is in the shape of a rectangle, where the length being twice as long as the width and the box must hold 9000 cubic inches of material?

##### 1 Answer

Feb 24, 2015

Let's begin by putting in some definitions.

If we call **volume**

Now for the **surfaces** (=material)

Top&bottom:

Short sides:

Long sides:

**Total area:**

Substituting for

To find the minimum, we differentiate and set

Which leads to

**Answer** :

Short side is

Long side is

Height is

*Check your answer!*