Open Box Investigation

25th January Math | Sara Ellis Introduction: The open box problem is regarding an open box made from a sheet of card. Identical sized squares are removed from the four corners of the card (shown in the diagram below). The aim of this investigation is to verify the size of the square removed that would make the largest volume for any given sheet of card, both square and rectangular. I will do this by finding a general formula which would work for finding the best size of square cut. Square Boxes In order to determine the size of square cut off from the card, I tried many different sizes on square boxes to find the size that would give the largest volume. To find the volume I have used the formula: Volume = Length x Width x Height To find the length and width I take two of the length of square cut from the total length/width of the box. The height is the same as the side length of square cut. Below are my results: 0x10 Square Side Length of Square (cm) 2 3 4 Length of Box 8 6 4 2 Width of Box 8 6 4 2 Height 2 3 4 Volume 64 72 48 6 To find the more precise length of square which I should cut, I have used the upper and lower bounds of the best length of square in the table above (in this case, 2cm). Side Length of Square .5 .6 .7 .8 .9 2 2.1 Length of Box 7 6.8 6.6 6.4 6.2 6 5.8 Width of Box 7 6.8 6.6 6.4 6.2 6 5.8

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  • Level: GCSE
  • Subject: Maths
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