• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12
  13. 13
    13
  14. 14
    14
  • Level: GCSE
  • Subject: Maths
  • Word count: 1432

To find out what size squares must be cut out of the corners of square and rectangle pieces of card to give the box it would create its optimum volume.

Extracts from this document...

Introduction

As a class we were given a mathematical problem to solve as our first bit of maths coursework for GCSE, it is called the open box problem. We have been asked to find out what size square we would have to cut out the corner of a piece of card, either square or rectangular, to find the optimum volume of that box. I will start at 1cm³ Square and work up in 1cm³.

         I would expect the optimum volume to most of the time be in the decimal places so I will have to look at all the decimal places between the highest volume I have and the highest one on one of its sides. During this experiment I will be looking for relationships between the length of the side and the volume of the box.

Aim:-  To find out what size squares must be cut out of the corners

...read more.

Middle

2.6=120.224

2.7=117.612

Optimum Volume=2

Mini Summary

I don’t think I have enough results so I’m going to do a 15*15 to increase my results.

15*15 Square

Height (cm²)

1

2

3

4

5

6

7

Volume (cm³)

169

242

243

196

50

36

7

2.1=244.944

2.2=247.192

2.3=248.768

2.4=249.696

2.5=250                                   Optimum Volume= 2.5 = 250

2.6=249.704

2.7=248.832

2.8=247.408

2.9=245.456

The diagram below will help you to understand my formulas and equations.

                        10cm (x)

10cm (x)

To find the base area of the square you use the equation (x-2h)(x-2h).

Take h as 1cm

(10-2*1)(10-2*1)=64cm²

To find the size of square to cut out of the corner on a square to find the optimum volume use the formula:- cut-out = Length of side / 6

...read more.

Conclusion

        The one similarity I found between the squares and rectangles comes from looking at the graphs I have from the results. Looking at the graphs I can see that they are similar in shape. They all peak in roughly the same area and then begin to fall quite rapidly, this is what I said was what I thought would happen in my prediction.

        With the squares I can see from the ones I have looked at that the squares all peak in the high ones and the low twos. Unlike with the rectangles I found a formula I can use with all squares. It tells me what size I should make the squares on the corners for any size square

...read more.

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Number Stairs, Grids and Sequences essays

  1. Marked by a teacher

    Opposite Corners. In this coursework, to find a formula from a set of numbers ...

    4 star(s)

    173 174 175 176 184 185 186 187 188 189 190 191 199 200 201 202 203 204 205 206 214 215 216 217 218 219 220 221 229 230 231 232 233 234 235 236 From the previous page, 124 � 236 = 29264 131 � 229 = 29999

  2. Marked by a teacher

    Opposite Corners

    4 star(s)

    z+12 z+13 z+14 (z+4)(z+30)=z�+34z+120 z+20 z+21 z+22 z+23 z+24 (z�+34z+120)(z�+34z)=120 z+30 z+31 z+32 z+33 z+34 Difference This proves that my prediction is correct. This also proves that the difference of a 4*5 rectangular box = 120 I predict for a 5*6 rectangular box the difference will equal 200.

  1. Marked by a teacher

    Opposite Corners

    3 star(s)

    22 30 31 32 Prediction I predict that when I 10x32=320 multiply a 3x3 30x12=360 rectangle (square) the Opposite corners will Have a difference of 40. 3x4 Rectangle 42 43 44 45 52 53 54 55 62 63 64 65 17 18 19 20 27 28 29 30 37 38

  2. Marked by a teacher

    In this piece course work I am going to investigate opposite corners in grids

    3 star(s)

    So again I have a multiple of 7. 9 10 11 12 16 17 18 19 23 24 25 26 30 31 32 33 Again 63 is a multiple of 7. 25 26 27 28 32 33 34 35 39 40 41 42 46 47 48 49 Yet again the answer is 63, a multiple of the number 7.

  1. Marked by a teacher

    To find a relationship between the opposite corners in various shapes and sizes.

    51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

  2. Investigate Borders - a fencing problem.

    for border number 6: First replace 'n' with 6. 4 y + ( 2 x 6 - 2 ) = 4 y + 10 Now you can replace the 'y' with an 'n' to have the formula, to find the number of squares, for border number 6.

  1. Investigate the difference between the products of the numbers in the opposite corners of ...

    so I for the 3x3 I will just try 2 shapes on the horizontal, 2 shapes on the vertical and 2 shapes on the diagonal, along with the random position to ensure accurate results. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

  2. Mathematical Coursework: 3-step stairs

    term 20. Thus making it's time consuming. After analysing the grids, the table of results and my prediction I have summed up an algebraic equation which would allow me to find out the total of any 3-step stair shape in a matter of minutes. The criterion of why I haven't explained what B stands for is because I haven't found it yet.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work