A box with a square base and no top is to be built with a volume of 4000 in3. Find the dimensions of the box that requires the least amount of material. How much material is required at the minimum?

Answer 1

V = x^2 h = 4000 so h = 4000/x^2

A = x^2 + 4 x h
A = x^2 + 4 x (4000/x^2)
A = x^2 + 16,000/x
dA/dx = 0 at max or min
0 = 2 x -16000/x^2

x^3 = 8000

x = 20
now do the rest