# How do you find the dimensions that minimize the amount of cardboard used if a cardboard box without a lid is to have a volume of #8,788 (cm)^3#?

##### 1 Answer

Feb 27, 2015

You set

The box will have a square bottom.

Then the amount of cardboard used will be:

For the bottom:

For the sides:

**Total area** :

The **volume** of the box=

Substituting that into the formula for the area

To find the minimum, we have to differentiate and set to

Substitute:

**Answer** :

The sides will be