Open Box Problem
Introduction In this project, I am aiming to: . Determine the size of square cut from any given square sheet of card which makes the volume of an open top box as large as possible. 2. Determine the size of square cut from any given rectangular sheet of card which makes the volume of the resulting open top box as large as possible 4 squares were cut from the paper (1 from each corner). It was then folded along the lines (see diagram), to make an open top cuboid. Different size squares being cut from the paper each time resulted in a different volume. I spent time ring to calculate the size of the square using trial and improvement. Firstly, I examined the size of cut that gave the largest volume of open box by using squared paper to test out some different sizes of squares and rectangles. I then used Microsoft Excel spreadsheets to calculate the lengths, depths and widths to give me the volume of the open box. I calculated the size of cut that would give me the greatest volume to 3 decimal places. To create the box, the equal size squares are cut from the four corners of the card, and it is then folded along the dotted lines. I then put the resultant data into tables to try and calculate relationships between things such as length and square cut. I then tried to calculate a formula that would give me the size of square that must be cut to give me the optimum volume of