Calculus › Optimisation problems › Boxes of maximum volume
Open-top box with minimum surface area
High school · ●●○○○ 20 pts
A container company makes an open-top rectangular box with a square base. The box must have a volume of . Let the side length of the square base be cm and the height be cm. (1) Find the value of that gives the minimum outer surface area. (2) Find the minimum surface area, in .