The open box problem.

... The Open Box Problem An open box is to be made from a sheet of card. Identical squares are cut off the four corners of the card, as shown below. The card is then folded along the dotted lines to make the box. The main aim is to determine the size of the square cut which makes the volume of the box as large as possible for any given rectangular sheet of card. I am going to begin by investigating a square with a side length of 20 cm. Using this side length, the maximum whole number I can cut off each corner is 9cm, as otherwise I would not have any box left. I am going to begin by looking into whole numbers being cut out of the box corners. The formula that needs to be used to get the volume of a box is: Volume = Length * Width * Height

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