A square base box

Question

The making of an open top box from a 20 inch by 20 inch sheet of metal.

1. write a formula for the volume of your new box.
2. What reaction should be placed on the domain of this function?

Answer 1

Cut equal size squares of side length x from each corner of the 20" by 20" piece of sheet metal and fold up the sides to get a box without a top.

The bottom of the box is a square with side length 20-2x and the height is x.

So, V = x(20-2x)(20-2x), where 0 < x < 10.