# The Open Box Investigation

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The Open Box Investigation The aim of this investigation is to find the largest volume within for an open box with any size square cut out I will be increasing the square cut out by 1cm until I reach a point where the volume decreases. At this point I will decrease the square cut out by 0.1cm until I reach the maximum volume. This will be done on several different grids until I see a pattern which I will then use to create a formula. I will record my results in a table for the different grids and record the peaks to try and establish a pattern. My initial grid size will be 12cm x 12cm and I will increase this as I continue my investigation. The volume will be calculated by multiplying the length by the width by the height. When I appear to reach a maximum volume I will try cut sizes 0.1cm smaller and larger than the cut size that appears to give the maximum volume. If the volume increases then I will make the cut size smaller or larger by 0.1cm again. I will repeat this for grid sizes of 18cm x 18cm and 24cm x 24cm. I have found the following results: Grid Size: 12cm x 12cm Cut Size Calculation Volume 1cm 10 x 10 x 1 100cm3 2cm 8 x 8 x 2 128cm3 3cm 6 x 6 x 3 108cm3 1.9cm 8.2 x 8.2 x 1.9 127.8cm3 2.1cm 7.8 x 7.8 x 2.1 127.8cm3 Grid Size: 18cm x 18cm Cut Size Calculation Volume 1cm 16 x 16 x 1 256cm3 2cm 14 x 14 x 2 392cm3 3cm 12 x 12 x 3 432cm3 4cm 10 x 10 x 4 400cm3 2.9cm 12.