• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

The Open Box Problem.

Extracts from this document...

Introduction

Mathematics GCSE                THE OPEN BOX PROBLEM

Craig Lochhead 11G

Problem

I have to find out the volume of a box by using at first a square sheet and then cutting out the corners at any length. The volume of the box will differ to the amount you cut off. I will then try to find the maximum volume of an open square box. After finding the maximum volume of a square I will investigate further using rectangles sheets to cut out square edges. I will also find out the maximum volume of a rectangle sheet as well. I will use formulas and graphs to help me find out the maximum volume of both a rectangle and a square and pick out patterns seen in the tables I will make.

...read more.

Middle

Question Two

Some examples on how cut out will look like in question two

10x20 cut out size 3

...read more.

Conclusion

        I think I could have improved my results and graphs if I was to do numbers such as 15, 25, 35 etc… this would have improved my graphs because there would have been more observations to write about. It would have made my formulas easy to pick out as well.

        I could have taken my experiment further by using other sizes. The sizes could have been more precise making my results and graphs more precise as well. There was a limited amount of shapes I could have due to the specifications of the problem because the shapes could have only been shapes with four right angle corners. Therefore leaving only two shapes to work on. The square and the rectangle.  

...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

    Mathematics Coursework: problem solving tasks

    3 star(s)

    So L = 4. The + shape spacers appear to be forming a square within the main square arrangement of each tile design. I will still need to continue in investigating a little further until I reach a conclusion where I can then determine my formula.

  2. Marked by a teacher

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

    10 X + 11 X + 12 X + 13 X + 20 X + 21 X + 22 X + 23 X + 30 X + 31 X + 32 X + 33 I will now test this by picking a random box and working out the other numbers in the box.

  1. Investigate Borders - a fencing problem.

    30 Common Difference nth Term Results My prediction was 30 which is the correct answer, for the number of squares needed for border number 6, and which also proves that the formula is in working order. Diagram of Borders of square: 5x1 Table of results for Borders of square: 5x1

  2. Mathematical Coursework: 3-step stairs

    Therefore I will take the pattern number of the total: > 46-6=40 > b= 40 To conclusion my new formula would be: > 6n+40 8cm by 8cm grid 57 58 59 60 61 62 63 64 49 50 51 52 53 54 55 56 41 42 43 44 45 46

  1. The patterns

    45 46 47 48 49 50 12 x 45 = 540 42 x 15 = 630 630 - 540 = 90 I shall now use letters to prove this correct X X+3 X+30 X+33 X(X+33)=X�+33X (X+30)(X+3)=X�+33x+90 (X�+33X+90) - (X�+33X) = 90 Size of Square Difference 2x2 10 3x3 40 4x4

  2. Open box problem

    30.93750 10 8 3 24.00000 10 8 3.25 17.06250 10 8 3.5 10.50000 10 8 3.75 4.68750 10 8 4 0.00000 From the table above it can clearly be seen that the biggest volume gained from a 10 by 8 piece of rectangular sheet is 52.5cm (2dp), this volume lies between the height of 1.25cm and 1.75cm.

  1. I am doing an investigation to look at borders made up after a square ...

    This shows that my rule is correct. 1 BY 5 5 5 5 5 5 5 4 4 4 4 4 5 5 4 3 3 3 3 3 4 5 5 4 3 2 2 2 2 2 3 4 5 5 4 3 2 1 1 1 1

  2. The Open Box Problem

    5 320 5 6 6 6 216 6 4 4 7 112 7 2 2 8 32 As you can see from the table the largest volume of the open box was with the cut of 3cm. This shows that the cut out square that gives the 18cm by 18cm box its largest volume is 3cm.

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