# Maximum box investigation

Extracts from this document...

Introduction

maximum box project Ellie Roy Mrs. Satguru MP2b Maths Introduction: This project is about finding the maximum volume of different boxes by investigating what the length of the corner square is. For part 1 we had to find the maximum volume of a box made from a 20 x 20 cm piece of paper. You had to make a box (without a lid) by cutting squares from the corners. The diagram to the left shows where the corner squares are (they are shaded in grey.) It is the size of these corner squares which impact the volume of the finished box. To solve part 1's problem I tried out different corner square lengths and recorder my results in a table. For part 2 we had to do the same thing, however we had to find the volume of a box made from a 24 x 24 cm, 15 x 15 cm, 10 x 10 cm and 36 x 36 cm piece of paper instead of a 20 x 20 cm paper. We also had to try out different corner square lengths and draw tables to show our results for this as well. Part 3 was a bit harder. We had to try and find a connection between the size of the corners cut out and the size of the original piece of paper. But I did manage to find something. Aim: my aim is to find out the largest possible volume of a box made from a 20x20 cm piece of paper. I also want to find the largest possible volume for a box that is made from a 15x15 cm piece of paper, a 24x24 cm piece of paper, a 10x10 piece of paper and a 36x36 piece of paper. If possible I would also like to find if there is a connection between the size of the corners cut out and the size of the original piece of paper. ...read more.

Middle

16.6 3.5 4.5 3.75 4.75 4.25 4.2 4.15 4.1 4.05 3.9 3.8 3.7 1011.5 1012.5 1020.9 998.7 1021.1 1022.1 1022.9 1023.5 1023.9 1023.5 1022 1019.6 As you can see from the table on the bottom of the previous page I didn't find a greater volume for the box. I tried a lot of different corner square lengths and I didn't find anything. So, the maximum volume for a box made from a 24 x24 cm piece of paper is 1024 cm�. The next size of paper I used was 10 x 10 cm. In the table below you will see the results I got. The first table shows the all the different volumes I got when the length of the side of the corner square was a whole number. The second shows the different volumes I got when the length of the side of the corner square also had decimal places. Length of the side of the corner square Length of the box Width of the box Height of the box Volume of the box (cm�) 1 2 3 4 8 6 4 2 8 6 4 2 1 2 3 4 64 72 48 16 As you can see the maximum volume for a box made from a 10 x 10 cm piece of paper is 72cm� (if the corner squares length is a whole number.) Once again I wanted to try out whether the volume would increase if the corner square length had decimal places. The results are in the table below. Length of the side of the corner square Length of the box Width of the box Height of the box Volume of the box (cm�) 2.5 2.25 2.1 1.5 1.75 1.8 1.25 1.3 1.4 5 5.5 5.8 7 6.5 6.4 7.5 7.4 7.2 5 5.5 5.8 7 6.5 6.4 7.5 7.4 7.2 2.5 2.25 2.1 1.5 1.75 1.8 1.25 1.3 1.4 62.5 68.1 70.6 73.5 73.9 73.7 70.3 71.2 72.6 From the table on the last page you can see I found a way of getting the box to have a higher volume. ...read more.

Conclusion

I used my calculator skills when I was finding the volume of the different boxes and when I was trying to find patterns. I used my division skills in part 3 as I found patterns by (for example) dividing the length of one side of the original piece of paper by the length of the side of the corner square. I used my multiplication skills when I was finding the volume of boxes and finding the area of the original piece of paper (in part 3.) I used my pattern finding skills and problem solving skills in part 3 when I was trying to find a connection between the original piece of paper and the corners that were cut out. I used trial and improvement skills in part 1an 2 when I was trying to find the maximum volume of the different boxes. I used my skills at finding volume in part 1 and 2 when I was finding the maximum volume of the different boxes. I used my skills at finding area in part 3 when I found that the area of the original piece of paper is 9 times as big as the area of all 4 corners that were cut out, and I used my table drawing skills through the entire project as we had to show all of our results in tables. I don't think I learned any new skills but I do think I did improve my old ones. I don't really think I learnt any new concepts either. I did find some general rules. I found that the length of one side of the original piece of paper is around 6 times larger than the length of one side of the corner square. I also found that the area of the original piece of paper is about 8 to 9 times larger than the area of the 4 corner squares. 11 ...read more.

This student written piece of work is one of many that can be found in our GCSE Open Box Problem section.

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