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The open box problem By Luke Johnston An open box is to be made from a sheet of card with identical squares cut of the corners to make a box: y x = corner length y = box length The card is then folded along the dashed lines to make the box. The aim of this activity is to determine the size of the cut out square which makes the largest volume for a square. Firstly I will find this in a square of y = 10cm To find the volume I will use this equation-Volume= Width x length x height Cut off (cm) width (cm) length (cm) height (cm) volume (cm²) 1 8 8 1 64 2 6 6 2 72 3 4 4 3 48 4 2 2 4 16 The maximum box volume is made from the cut out square of 2cms. I will now try between 1-2 cm because the highest volume is somewhere between them. Cut off (cm) width (cm) length (cm) height (cm) volume (cm²) 1.1 7.8 7.8 1.1 66.924 1.2 7.6 7.6 1.2 69.312 1.3 7.4 7.4 1.3 71.188 1.4 7.2 7.2 1.4 72.576 1.5 7 7 1.5 73.5 1.6 6.8 6.8 1.6 73.984 1.7 6.6 6.6 1.7 74.052 1.8 6.4 6.4 1.8 73.728 1.9 6.2 6.2 1.9 73.036 2 6 6 2 72 The highest value of x is 1.7, but once again I will find a...

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