The Open Box Problem

I had the task of making a box out of an A4 piece of paper with the largest possible volume.

First of all I made a box out of an A4 piece of paper. To do this I had to cut squares out of each corner of the paper and fold up the sides.

I used random measurements in this test to see the results. I found that the size of the squares I cut out of the corner changed the volume of the box I made, so, using a spreadsheet I tried to find the maximum volume.

I first found out the box volumes for box corner sizes 0 – 100mm. I found out that 40mm corners made the largest volume.

To find the measurements that gave the biggest volume possible I put more accurate numbers into my spreadsheet.

Instead of going up in10mms, I started at 35mms and went up to 45mms in 1cm measurements. I found that using 40mm corners still produced best results.

I still was not happy with my results. So to make them more accurate I used decimal points, centimetres and millimetres. I started off using 1 decimal place.

40.4mm produced the largest volume. The graph shows my results

To produce more accurate results still, I used 2 decimal places, starting at 40.41mm, going up to 40.49mm.

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The Open Box Problem

I first found out the box volumes for box corner sizes 0 – 100mm. I found out that 40mm corners made the largest volume.

To find the measurements that gave the biggest volume possible I put more accurate numbers into my spreadsheet.

Instead of going up in10mms, I started at 35mms and went up to 45mms in 1cm measurements. I found that using 40mm corners still produced best results.

I still was not happy with my results. So to make them more accurate I used decimal points, centimetres and millimetres. I started off using 1 decimal place.

40.4mm produced the largest volume. The graph shows my results

To produce more accurate results still, I used 2 decimal places, starting at 40.41mm, going up to 40.49mm.

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Instead of going up in10mms, I started at 35mms and went up to 45mms in 1cm measurements. I found that using 40mm corners still produced best results.

I still was not happy with my results. So to make them more accurate I used decimal points, centimetres and millimetres. I started off using 1 decimal place.

40.4mm produced the largest volume. The graph shows my results

To produce more accurate results still, I used 2 decimal places, starting at 40.41mm, going up to 40.49mm.

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