The Open Box Problem
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| Submitted: Thu Jul 11 2002
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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. Box Made From A4 paper Corner Length Width Height Volume mms mms mms mms mm3 0 297 210 0 0 10 277 190 10 526300 20 257 170 20 873800 30 237 150 30 1066500 40 217 130 40 1128400 50 197 110 50 1083500 60 177 90 60 955800 70 157 70 70 769300 80 137 50 80 548000 90 117 30 90 315900 100 97 10 100 97000 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. Box Made From A4 Paper Corner Length Width Height Volume mms mms mms mms mm3 35 227 140 35 1112300 36 225 138 36 1117800 37 223 136 37 1122136 38 221 134 38 1125332 39 219 132 39 1127412 40 217 130 40 1128400 41 215 128 41 1128320 42 213 126 42 1127196 43 211 124 43 1125052 44 209 122 44 1121912 45 207 120 45 1117800 Instead of going up in10mms, I started at 35mms and...


