• 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

The Open Box Problem AIM To determine the size of a square cut which makes the volume of the box as large as possible for any given rectangular sheet of card. I should also be able to come up with a formula to ..... ...read more.

Middle

This means that I have to work out the size of the open box which has the largest possible volume. Z (mm) Y (mm) X (mm) VOLUME OF BOX (mm�) 100 5 90 40500 100 10 80 64000 100 15 70 73500 100 20 60 72000 Z (mm) ...read more.

Conclusion

X (mm) VOLUME OF BOX (mm�) 100 17.1 65.8 74036.844 100 17.2 65.6 74017.792 100 17.3 65.4 73994.868 Z (mm) Y (mm) X (mm) VOLUME OF BOX (mm�) 100 17.21 65.58 74015.67344 100 17.22 65.56 74013.51619 100 17.23 65.54 74011.32027 Z (mm) Y (mm) X (mm) VOLUME OF BOX(mm�) 100 17.221 65.558 74013.29834 100 17.222 65.556 74013.0801 ...read more.

The above preview is unformatted text

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)

    I will start with putting up tiles in a straight line, then look at two rows of tiles, then three rows of tiles and so fourth. As placing the results into table form proved successful, I will repeat the process again.

  2. Investigate Borders - a fencing problem.

    needed for border number 6 using the formula, I found out, above: nth term = 4 x 6 + 4 = 28 Common Difference nth Term Results My prediction was 28 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.

  1. Open box problem

    RECTANGLE Length (L) cm Width (W) cm Height (X) cm Volume cm3 10 8 0 0.00000 10 8 0.25 17.81250 10 8 0.5 31.50000 10 8 0.75 41.43750 10 8 1 48.00000 10 8 1.25 51.56250 10 8 1.5 52.50000 10 8 1.75 51.18750 10 8 2 48.00000 10 8 2.25 43.31250 10 8 2.5 37.50000 10 8 2.75

  2. Investigate the size of the cut out square, from any square sheet of card, ...

    32 divided by 3= 10.66666 (recurring) 16 divided by 3= 5.333333 (recurring) 3 divided by 32= 0.09375 3 divided by 16= 0.1875 This is my second investigation: 20cm by 10cm piece of card In the table above, you can see the largest volume produced (1.92.4499cm cubed)

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

    With the term-to-term rule I can predict the 6th border. As you can see, number of numbered squares goes up in 4. To work out the rule I will multiply 1 by 4. Then I will see if the answer is 12.

  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.

  1. Open Box Problem.

    I used the same calculations do work out the volume of the open box except this time, I substituted the number 24 for the number 30. As you can see, the scatter diagram below also shows that the maximum volume of a 30cm by 30cm square occurs when the cut x is equal to 5.

  2. The Open Box Problem

    For each size of A (original piece of card) the volume increases to a maximum point decreases there after. Firstly I will find a general rule for the volume in terms of X and A. To find a general rule for the volume of any box, I will be using the following letters in place of numeric values.

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