Math CentralQuandaries & Queries


Question from William, a student:

Hi, I have this math question that says construct a cereal box that has a volume of 12000cm3 and the surface area of the box has to be between 3200cm2 and 400cm2, I found some dimensions that are 20 by 20 by 30 and it works, but when I attempt to make the box, or make a net I would need this hugh piece of paper/cardboard, which I don't have, is there an easier way to find different dimensions so I don't need a hugh piece of paper to create a net easily? Because i've tried trial and error but it has taken to long and I cant find anything,else, that's reasonable.


If the box is required to have a volume of 12000 cm3 then the box with minimum surface area is a cube with sides of length cube root of 12000 = 22.89. (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 cm2 and hence the total surface area is 3144.89 cm2. Your 20 by 20 by 30 box has a surface area of 3200 cm2 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.


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