The Open Box Problem

... Part 1: Square Ryan Simmons For any sized square sheet of card investigate the size of the cut out square that makes an open box of the largest volume. The first square to be tested has measurements of 30 x 30 cm. For cut sizes I will start from the smallest (whole) number possible (1cm) I will then work my way up to find which size cut gives the box the largest volume. So far as the size of the cuts increase the volume increases. I predict that a cut size of 3 x 3 cm will give an even bigger volume for the box. A cut of 3 x 3 cm gives a volume of 1728 cm3, hence my prediction was right. 3cm x 24cm x 24cm = 1728 cm³ The prediction was right and so far there is no obvious pattern between the cut sizes and

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