A lidless box with square ends is to be made from a thin sheet of metal. Determine the least area of the metal for which the volume of the box is 3.5 m^3.

Answer 1

If the box has ends of side x and length y, then x^2 y = 7/2
the area is a = 2x^2 + 4xy = 2x^2 + 4x(7/2x^2) = 2x^2 + 14/x
da/dx = 4x - 14/x^2
Now just find where da/dx=0