Question

If 2000 square centimeters of material is available to make a box with a sqare base and an open top, find the largest possible volume of the box.

Answer 1

Let be x the side of the square base of the box and h the height. S=2000 cm2
We try to find max x^2*h
with 4*x*h+x^2<2000
This is a rather long optimization problem but you find in the end that it's the cube with a side of x=20

Answer 2

It's a cube so h=x so 5x^2<2000 ie x^2<400 ie x<20
So x=20cm is the max value for the side.

Answer 3

^ Good work