An open box is formed from an 80cm by 80cm peice of metal by cutting four identical squares from the corners and folding up the sides. Express the volume of the box in terms of x. Then describe how you could find the maximum possible volume.

Answer 1

The height of the box becomes x, and each side is reduced by 2x. Therefore the volume is given by V = x(80-2x)(80-2x) because the original length and width are both 80.

Answer 2

40

Answer 3

An open box is to be made from a flat piece of material 11 inches long and 5 inches wide by cutting equal squares of length x from the corners and folding up the sides.
Write the volume Vof the box as a function of x. Leave it as a product of factors, do not multiply out the factors.