An open cylindrical can is made from iron sheet to hold 4000 cm^3 of water. The bottom of the can is cut from a square sheet of iron.
(a) Show that the total area A (cm^2) of the material used can be expressed in terms of the radius r (cm) of the can as A = 4r^2 + 8000/r .
(b) Find the radius of the can that requires the least amount of material and the material used.