The Open Box Problem Essay Example

The Open Box Problem Essay I have to find out the volume of a box by using at first a square sheet and then cutting out the corners at any length. The volume of the box will differ to the amount you cut off. I will then try to find the maximum volume of an open square box. After finding the maximum volume of a square I will investigate further using rectangles sheets to cut out square edges. I will also find out the maximum volume of a rectangle sheet as well. I will use formulas and graphs to help me find out the maximum volume of both a rectangle and a square and pick out patterns seen in the tables I will make. (All measurements will be measured in centimetres)Question OneThis is an example of what I will do.1010 cut out size 2cm20x20 cut out size 3cm30x30 cut out of 4 cmQuestion TwoSome examples on how cut out will look like in question two10x20 cut out size 31030 cut out size 42030 cut out size 5ConclusionAll the formulas I found were based on the results and graphs shown. I used both my graphs and result s in question 1 to find the maximum cut out size for maximum volume and the formula for the maximum volume if using a square. The reason why I could not find the formula for the maximum cut out size for two lengths is because, using only the results and graphs, it is impossible to find the maximum cut out size. This is because the two different lengths have no relation with each other. Both sides of the rectangle are variables that have nothing in common with each other. This is because both variables can change independently.Although my results cannot show a formula there are other ways of finding a formula such as calculus. As background information to this coursework I have gotten help to prove that calculus does work in this formula.Using the formulas that I have got I can now work out the maximum cut out size to find the volume or I can find out the maximum volume of any open square box. I can also find the maximum volume of any size rectangle using my formula.Observation and E valuationThere were a lot of patterns that were obvious in my graphs but not so obvious in my results table. For example there was a straight rise in the first graph and there was an exact distance of 1.66 recurring for the cut out which helped me find my formula.I think I could have improved my results and graphs if I was to do numbers such as 15, 25, 35 etc this would have improved my graphs because there would have been more observations to write about. It would have made my formulas easy to pick out as well.I could have taken my experiment further by using other sizes. The sizes could have been more precise making my results and graphs more precise as well. There was a limited amount of shapes I could have due to the specifications of the problem because the shapes could have only been shapes with four right angle corners. Therefore leaving only two shapes to work on. The square and the rectangle.