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The Open Box Problem  

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The Open Box Problem I am going to investigate the size of the square cut which makes the volume of the box as large as possible for any given rectangular sheet of card. First I am going to investigate the size of the cut out square which makes an open box of the largest volume for any sized square 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 a box. To find volume the following formula is needed: Volume=length x width x height. To investigate the first square sheet of card, I am going to use a square with the length of each side as 18cm². The practical method would be to make a box and obtain the volume from that, and changing the size of the cut out squares for each trial. For...

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