maximum length of rectangles and volume

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Ben Patience                Maths Coursework

Conclusion

When I began this take of trying to find out the maximum length of rectangles in different my initial task was simply to find a formula to relate to the rectangles. To solve the problem I used computer programmes such as Microsoft Excel and Microsoft Word to present the data and my findings. I initially chose to work with squares 8x8, 9x9, 13x13, and 25x25 for the simple fact that I was looking for some connection between all types of squares.

When I used the computer I headed my columns on my spreadsheets as follows:

Side1 (length), Side2 (width), Cut out, Length, Width, Height, Volume. I used these in this order to try and determine the formula and maximum cut out length for each type of square and rectangle.

To work out different volumes I used different formulas. I worked out these formulae by simple trial and error. This did take some time but eventually came out more accurate.

I worked with different numbers (such as, a whole number, to 1 decimal place, to 2 decimal places and to 3decimal places) to make the maximum cut out lengths more accurate when dealing with decimal places. I could have made it even more accurate by doing it to 4 decimal places by 3decimal places was only necessary to be drawing conclusions for this assignment.

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I noticed that when I found out the maximum size volumes for both squares and rectangles that the bigger the square the bigger the volume. I also noticed that to find out the biggest volume the rectangle or square needed to be as equal in sides as possible to work out the maximum volume and cut out size.

I expected that the maximum volumes would become greater as the square or rectangle became bigger and that the cut out length would not be very big because it would make the box size smaller it the cut out length was ...

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