An open top box with a square base is to be constructed so that it will have a volume of 2m^3. What dimensions should be used to construct this box so that a minimum amount of material is used?

Answer 1

Let x = length of a side of the base and let y = height

Then x²y = 2. So, y = 2/x².

Minimize S = surface area

S = Area of base + area of the four sides

S = x² + 4xy = x² + 8/x

Take the derivative of S with respect to x and see where S' = 0.