If 1300 square centimeters 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

If the base has side x, and height h, we know that
x^2 + 4xh = 1300
So, h = (1300-x^2)/(4x)
The volume is just v = x^2h = x/4 (1300-x^2)
So now just find where dv/dx = 0

Answer 2

The answer is 4510.28 cubic centimeters.