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Mathematics GCSE coursework The open box problem An open box is made from a sheet of card Identical squares cut off the four corners of the card The card is then folded along lines to make an open box. The main aim of the activity is to determine the size of the square cut which makes the volume of the box as large as possible for any given square sheet of card. Part 1 I have drawn tables for my squares. I have tested four squares; 5cm square, a 10cm square, a 20cm square, a 40cm square. I have decided against trial and improvement. As this method can is time consuming so I have used gone up in 0.5cm each time for the size of x (the cut out size) then calculated the size of v (volume). In one table of values I have gone to 5 decimal places to prove my relationship is correct. The volume...

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