Mathematical models: constructing an open box

Question

An open box with a square base to be made of a square piece of cardboard 24 inches on 24 inches on a side by cutting out a square from each corner an turning up the sides. Express the volume v of the box as a function of the length x of the square cut from each corner. 

Answer 1

Cutting a square of side "x" from the flat cardboard and turning this up all around the cardboard piece, leaves a side of (24-2x) and a height of (x).

Then the volume of the box would be V = x(24-2x)²