



 
William, If the box is required to have a volume of 12000 cm^{3} then the box with minimum surface area is a cube with sides of length . (The fact that a box with a fixed volume has a minimum surface are if it is a square is an advanced calculus problem and I can't show you an easy proof.) This cube has 6 faces, each of surface area 22.89 × 22.89 cm^{2} and hence the total surface area is 3144.89 cm^{2}. Your 20 by 20 by 30 box has a surface area of 3200 cm^{2} so it is almost as small as possible. I think you are going to have to make your box using 6 pieces of cardboard and some tape. Harley  


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