• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 1826

First Problem,The Open Box Problem

Extracts from this document...

Introduction

In this investigation, I will be investigating the maximum volume, which can be made from a certain size square piece of card, with different size sections cut from their corners. The types of cubes I will be using are all open topped boxes.

The size sections that I will be cutting from the square piece of card will all be the same size. The section sizes will go up to half of the original size of card. I will only go up to this size, because it is physically impossible to cut square sections, with sides over half the length of the original shape.

During this investigation, I will not account for the ‘tabs’, which would normally be needed to hold the box sides together.

...read more.

Middle

2.8

2.8

4.704

0.7

0.7

2.6

2.6

4.732

0.8

0.8

2.4

2.4

4.608

0.9

0.9

2.2

2.2

4.356

1.0

1.0

2.0

2.0

4.000

1.1

1.1

1.8

1.8

3.564

1.2

1.2

1.6

1.6

3.072

1.3

1.3

1.4

1.4

2.548

1.4

1.4

1.2

1.2

2.016

1.5

1.5

1.0

1.0

1.500

1.6

1.6

0.8

0.8

1.024

1.7

1.7

0.6

0.6

0.612

1.8

1.8

0.4

0.4

0.288

1.9

1.9

0.2

0.2

0.076

2.0


5cm by 5cm, piece of square card

Length of the section (cm)

Height of the section (cm)

Depth of the section (cm)

Width of the section (cm)

Volume of the cube (cm3)

0.1

0.1

4.8

4.8

2.304

0.2

0.2

4.6

4.6

4.232

0.3

0.3

4.4

4.4

5.808

0.4

0.4

4.2

4.2

7.056

0.5

0.5

4.0

4.0

8.000

0.6

0.6

3.8

3.8

8.664

0.7

0.7

3.6

3.6

9.072

0.8

0.8

3.4

3.4

9.248

0.9

0.9

3.2

3.2

9.216

1.0

1.0

3.0

3.0

9.000

1.1

1.1

2.8

2.8

8.624

1.2

1.2

2.6

2.6

8.112

1.3

1.3

2.4

2.4

7.488

1.4

1.4

2.2

2.2

6.776

1.5

1.5

2.0

2.0

6.000

1.6

1.6

1.8

1.8

5.184

1.7

1.7

1.6

1.6

4.352

1.8

1.8

1.4

1.4

3.528

1.9

1.9

1.2

1.2

2.736

2.0

2.0

1.0

1.0

2.000

2.1

2.1

0.8

0.8

1.344

2.2

2.2

0.6

0.6

0.792

2.3

2.3

0.4

0.4

0.368

2.4

2.4

0.2

0.2

0.096

2.5


6cm by 6cm, piece of square card

Length of the section (cm)

Height of the section (cm)

...read more.

Conclusion

So if A = the size of the side I start with, and X = the size of the cut out, then my results can be described by the following equation:

X = 1/6A

To prove it further, I have decided to test my rule with one larger number, 100cm x 100cm. To test this equation, on the very large square gives the results below:

X = 1/6100

X = 16.667 cm

       VOL. = X ( A - 2X ) ( B - 2X )

= 16.667 ( 100 - 2 x 16.667 ) ( 100 - 2 x 16.667 )

= 16.667 ( 100 - 33.334 ) ( 100 - 33.334 )

= 16.667 x 66.666 x 66.666

= 74074.074 cm3

If I make X slightly bigger or smaller, then the volume should decrease. I will use X = 16.6, and X = 16.75.

 Vol. = X ( A - 2X ) ( B - 2X )

= 16.6 ( 100 - 33.2 ) ( 100 - 33.2 )

= 16.6 x 66.8 x 66.8

= 74073.184

 Vol. = X ( A - 2X ) ( B - 2X )

= 16.75 ( 100 - 33.5 ) ( 100 -33.5 )

= 16.75 x 66.5 x 66.5

= 74072.687

These are both smaller than my predicted value, and therefore my prediction is correct.

...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)

    I have titled each table of results with the symbol used to represent the shape of the spacer it relates to. L Shape Spacer Results Term Tile Arrangement Term x common difference Sequence Difference 1 1 x 1 1 x 0 = 0 4 4 - 0 = 4 2

  2. Mathematical Coursework: 3-step stairs

    Therefore I will take the pattern number of the total: > 58-6=52 > b= 52 To conclusion my new formula would be: > 6n+52 8cm by 8cm 9cm by

  1. Investigate Borders - a fencing problem.

    Common difference = 4 First term = 8 Formula = Simplification = Experiment I will try to find the number of squares 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

  2. Open box. In this investigation, I will be investigating the maximum volume, which can ...

    2.2 2.2 1.936 0.5 0.5 2.0 2.0 2.000 0.6 0.6 1.8 1.8 1.944 0.7 0.7 1.6 1.6 1.792 0.8 0.8 1.4 1.4 1.568 0.9 0.9 1.2 1.2 1.296 1.0 1.0 1.0 1.0 1.000 1.1 1.1 0.8 0.8 0.704 1.2 1.2 0.6 0.6 0.432 1.3 1.3 0.4 0.4 0.208 1.4 1.4

  1. Open box problem

    Length (L)cm Width (W)cm Height (X)cm Volume cm3 (2dp) 8 8 1.05 36.55050 8 8 1.1 37.00400 8 8 1.15 37.36350 8 8 1.2 37.63200 8 8 1.25 37.81250 8 8 1.3 37.90800 8 8 1.35 37.92150 8 8 1.4 37.85600 8 8 1.45 37.71450 As it can clearly be

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

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

  1. The Open Box Problem

    Below I have written a formula of this method. This method helped me find the largest volume of the square much faster because I did not have to construct nets. (length-2?)� x ? (? is the cut out square length) Because the size of the square sheet of card is 18cm�, the maximum length the cut out square can

  2. Algebra Investigation - Grid Square and Cube Relationships

    = Top Right (TR) + Bottom Left (BL) As also shown by the summary boxes and examples above, the formula for the top right number remains constant, and is linked with the width, w, of the box in the following way: Formula 2: Top Right (TR)

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