# What will the dimensions of the resulting cardboard box be if the company wants to maximize the volume and they start with a flat piece of square cardboard 20 feet per side, and then cut smaller squares out of each corner and fold up the sides to create the box?

##### 1 Answer

Mar 24, 2015

Suppose that the squares removed from each corner are

When these are folded up they give a box with a height of

and a base of

for a volume

To find the critical point(s) take the derivative of

Since

The resulting box will be