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  • Level: GCSE
  • Subject: Maths
  • Word count: 1718

Trays. The first square I will investigate is a 24cm x 24cm square. My prediction is that the shopkeepers statement will also be true for a square of this size.

Extracts from this document...

Introduction

TRAYS Firstly I am going to investigate the shopkeeper's statement. If the width of the side of the tray is represented by the letter w then we have: So The volume of the tray = w (18cm - 2w)(18cm -2w) Results Table Width of Side (cm) Length of base (cm) Volume (cm3) Area of Side (cm2) Area of all sides(cm2) Area of base (cm2) 1 16 256 16 64 256 2 14 392 28 112 196 3 12 432 36 144 144 4 10 400 40 160 100 5 8 320 40 160 64 6 6 216 36 144 36 7 4 112 28 112 16 8 2 32 16 64 4 Conclusion The results table and the diagrams above prove that the shopkeeper's statement is true as you can see by the blue highlighted part of the results table above. Now I have discovered that the shopkeeper's statement is true I will investigate this further by finding out if the statement is true for other sized squares. 24cm x 24cm square The first square I will investigate is a 24cm x 24cm square. My prediction is that the shopkeeper's statement will also be true for a square of this size. ...read more.

Middle

400 100 11 8 704 88 352 64 12 6 432 72 288 36 13 4 208 52 208 16 14 2 56 28 112 4 Conclusion The Results table above proves that the shopkeeper's statement is true. The size of this square is also a multiple of 6. So this leads me to believe that the shopkeeper's statement is only true for trays which lengths are multiples of 6. Now I will pick a random number which is not a multiple of 6 to make sure that the shopkeeper's statement does not work for this square. I predict that it will not work. 34cm x 34cm Square I If the width of the sides is represented by W then we have: So the volume of the tray = w(34cm - 2w)(34cm - 2w) Results Table Width of Side (cm) Length of base (cm) Volume (cm3) Area of Side (cm2) Area of all sides(cm2) Area of base (cm2) 1 32 1024 32 128 1024 2 30 1800 60 240 900 3 28 2352 84 336 784 4 26 2704 104 416 676 5 24 2880 120 480 576 6 22 2904 132 528 484 7 20 2800 140 560 400 8 18 2592 144 576 324 9 16 2304 144 576 256 10 14 1960 140 560 196 11 12 1584 132 ...read more.

Conclusion

= the maximum volume that sized tray can possibly have 12 x 12 x 3 = the maximum volume that sized tray can possibly have 432 = the maximum volume that sized tray can possibly have The above working out proves that the formula works for a 18cm x 18xcm square as you can see by the results table. Now I will check the formula using the 30cm x 30cm square (L/3 x 2)(L/3 x 2)(L/6) = the maximum volume that sized tray can possibly have (30/3 x 2)(30/3 x 2)(30/6) = the maximum volume that sized tray can possibly have (10 x 2)(10 x 2)(5) = the maximum volume that sized tray can possibly have 20 x 20 x 5 = the maximum volume that sized tray can possibly have 2000 = the maximum volume that sized tray can possibly have The above working out proves that the formula works for a 30cm x 30cm square as well. So I believe that this formula will work for any tray which the shopkeeper's statement is correct for. OVERALL CONCLUSION My overall conclusion is that the shopkeeper's statement was correct for an 18cm x 18cm square and any other square with a length which is a multiple of 6. I have also found out a formula and proved that it is correct. ...read more.

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