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

Maximum Box Investigation

Extracts from this document...

Introduction

Maximum Box Investigation Question: You have a square sheet of card 24cm by 24cm. You can make a box (without a lid) by cutting squares from the corners and folding up the sides. What size corners should you cut so that the volume of the box is as large as possible? The first step to evaluating the maximum possible volume that the box could contain is to find the area of the paper. This is simply 24cm x 24cm = 576cm�. Now that we have the area, it is easy to evaluate the maximum volume in a variety of different shapes. ...read more.

Middle

To find the volume of this particular cube, we need to cube 10.73 which gives us 1235.37. The volume of this cube is 715.575 cm�. However, the question instructs to fold and cut, which will need a list of results in a table: Table for card 24cm x 24cm Length of the side of the corner square (cm) Dimensions of the open box (cm) Volume of the box (cm�) 1 22 x 22 x 1 484 2 20 x 20 x 2 800 3 18 x 18 x 3 972 4 16 x 16 x 4 1024 5 14 x 14 x 5 980 6 12 x 12 x 6 ...read more.

Conclusion

Dimensions of the open box (cm) Volume of the box (cm�) 1 13 x 13 x 1 169 2 11 x 11 x 2 242 3 9 x 9 x 3 243 4 7 x 7 x 4 196 5 5 x 5 x 5 125 Investigate the situation when the card is not square. Take rectangular cards where the length is twice the width (20 x 10, 12 x 6, 18 x 9 etc.) Again, for the maximum volume is there a connection between the size of the corners cut out and the size of ...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. Algebra Investigation - Grid Square and Cube Relationships

    n+2(w-1)+2g(h-1) Simplifies to: n n+2w-2 n+2gh-2g n+2w+2gh-2g-2 Stage A: Top left number x Bottom right number = n(n+2w+2gh-2g-2) = n2+2nw+2ghn-2gn-2n Stage B: Bottom left number x Top right number = (n+2gh-2g)(n+2w-2) = n2+2nw-2n+2ghn+4ghw-4gh-2gn-4gw+4g = n2+2nw+2ghn-2gn-2n+4ghw-4gh-4gw+4g Stage B - Stage A: (n2+2nw+2ghn-2gn-2n+4ghw-4gh-4gw+4g)-(n2+2nw+2ghn-2gn-2n)

  2. Step-stair Investigation.

    It was this: n ??r = r =1 I this formula the sigma means "the sum of". So the formula means the sum of r (the number you start at) to n ( the number you finish at). The r = bit means the sum of all the numbers between r and n when placed in ascending order.

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

    To work out the rule I will multiply 1 by 4. Then I will see if the answer is 10. In this case it isn't so I will have to add 6 to get to 10. So my rule is 4B+6.

  2. My aims throughout this investigation are for each step stair is to investigate the ...

    The total is 56. The total from the previous grid is 50. I have picked up on one pattern so far. This is the difference between 50 and 56 is '6'. Although I cannot be completely sure that this difference is constant all the way through.

  1. Open Box Problem.

    As the formula of length/6 seems to have worked for both the squares before, I will use that equation to predict the cut of x, which will give the biggest volume for a 36cm by 36cm square: Length/width of square 36 4 6 = 6 Therefore, according to this equation,

  2. Boxes made in the shape of a cube are easy to stack to make ...

    I am going to try halving N2. B= 1 3 6 10 15 1/2 N2= 0.5 2 4.5 8 12.5 Whilst trying to find out the formula I noticed that to make B from 1/2 N2 all you need to do is add 1/2 L.

  1. For my investigation I will be finding out patterns and differences in a number ...

    I guess that the difference for the 6x6 squares will be 250 and the difference for the 7x7 squares will be 360. Here are some of the results I found for the 6x6 squares as you can see I have done more then one so that I can prove the difference.

  2. The Open Box Problem

    These show that the maximum volume for a square of width 12cm is obtained when x=2. Width of square Value of x to give maximum volume 6 1 12 2 I have noticed that so far, my results would suggest that the maximum volume if given when x is 1/6th of the width of the square sheet of card.

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