Question

If 10,800 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Answer 1

surface area of box = x^2 + 4xh = 10800 whereby = side of base and h = height of box
h = (10800 - x^2) / 4x

V = x^2 * h
V = x(10800 - x^2) / 4
V = 2700x - 0.25 x^2
now you can use calculus to find maximum volume

Answer 2

* where x = side of base

Answer 3

ooh - error in last line
V = 2700x - 0.25x^3