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The Open Box Problem
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| Submitted: Thu Jul 11 2002
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The Open Box Problem AIM To determine the size of a square cut which makes the volume of the box as large as possible for any given rectangular sheet of card. I should also be able to come up with a formula to ..... INVESTIGATING SQUARE SHEETS OF CARD 1. For any sized square sheet of card, investigate the size of the cut out square which makes an open box of the largest volume. USING A 100MM SQUARE SHEET OF CARD I will begin this investigation by working out the size of the square cut which makes an open box of the largest volume, using a 100mm square sheet of card . This means that I have to work out the size of the open box which has the largest possible volume. Z (mm) Y (mm) X (mm) VOLUME OF BOX (mm³) 100 5 90 40500 100 10 80 64000 100 15 70 73500 100 20 60 72000 Z (mm) Y (mm) X (mm) VOLUME OF BOX (mm³) 100 15 70 73500 100 16 68 73984 100 17 66 74052 100 18 64 73728 Z (mm) Y (mm) X (mm) VOLUME OF BOX (mm³) 100 17.1 65.8 74036.844 100 17.2 65.6 74017.792 100 17.3 65.4 73994.868 Z (mm) Y (mm) X (mm) VOLUME...
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