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• Level: GCSE
• Subject: Maths
• Word count: 3834

# Maximum box investigation

Extracts from this document...

Introduction

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.

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5 star(s)

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