• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 3040

When the area of the base is the same as the area of the four sides, the volume of the tray will be a maximum.

Extracts from this document...

Introduction

Maths Coursework Algebra-Investigating Trays Statement: The shopkeeper says, "When the area of the base is the same as the area of the four sides, the volume of the tray will be a maximum." Aim: To prove the shopkeeper's statement true. Task: To investigate this claim and investigate further. 18 x 18 I firstly started my trays investigation by drawing a net for a square measured 18cm by 18cm. I then cut out this net square, after it had been cut out I cut off 1cm off each of the four corners. This was so the tray would join together. I then calculated the area of the base. The formula I used to calculate the area of the base was: lxb For example: Area of Base, tray 1 16x16=256cm After this I then went on further to find the area of the four sides, as I had used this square before. I then used the formula lx4 to find the areas of the four sides, for example: 16x4=64cm I then calculated the volume of the tray. The calculations I used to find out the volume of the tray were: 14x14=256cm = 256x2=512cm The formula I used to calculate this was: lxbxh. Height: Base Length: Volume: Base Area: Area of 4 sides: 1cm� 16cm� 256cm 256cm 1x16x4=64cm 2cm� 14cm� 392cm 196cm 2x14x4=112cm 3cm� 12cm� 432cm 144cm 3x12x4=144cm 4cm� 10cm� 400cm 100cm 4x10x4=160cm 5cm� 8cm� 320cm 64cm 5x8x4=160cm 6cm� 6cm 216cm 36cm 6x6x4=144cm 7cm� 4cm 112cm 16cm 7x4x4=112cm 8cm� 2cm 32cm 4cm 8x2x4=64cm The tray that has the maximum volume is tray 3 and the area of this base equals to the area of the 4 sides which shows that the shop keeper's statement is true. ...read more.

Middle

Height: Base length: Volume: Base Area: Area of 4 sides: 1 16 x 6 96cm 96cm 16x6x4=348cm 2 14 x 3 84cm 42cm 14x3x4=168cm 3 14 x 4 168cm 56cm 14x4x4=224cm 4 12 x 2 96cm 24cm 12x2x4=96cm This is a graph showing all the results for each of the headings on the top of the table and for each height. This table shows that the maximum volume is when the height is 3cm but the area of the base does not equal to the area of the 4 sides. The after completing this tray I done another tray this time using halves to cut off the corners of the tray. 20x10 This is the net that I cut for the 15 by 5 and cut off halve e.g. 0.5, 1, 1.5 etc of each corner were it is marked on the rectangle. Height: Base length: Volume: Base Area: Area of 4 sides: 0.5cm 16x8 64cm 128cm 16x8x0.5x4=256cm 1cm 16x8 128cm 128cm 16x8x4=512cm 1.5cm 15x6 135cm 90cm 15x6x1.5x4=540cm 2cm 13x4 204cm 52cm 13x4x4=208cm 2.5cm 11x2 55cm 22cm 11x2x2.5x4=220cm 3cm 9x0 27cm 9cm 9x0x4=36cm This table shows the results that I got for cutting out each corner of the tray. The reason why I cut off 0.5 and then went on to cut off 1cm was because this why a pattern was formed for me to find out the maximum volume and are of the 4 sides. The maximum volume was when the height was 2cm, the area of the base though did not equal to the area of the 4 sides. The method that I used to calculate the volume was Lxbxh e.g. 13x3x0.5=19.5cm The formulas that are needed for these rectangle trays is only one formulas which is X 6 Most of the trays ...read more.

Conclusion

that I used the same method to calculate each volume, area of base and the area of the 4 sides therefore I got some accurate pieces of results also I got some good graphs which show all the area of the base, the maximum volume and the volumes and the area of the 4 sides they also show that the area of the base and 4 sides equal to the maximum volume. The investigation also went well because I got all the algebra formulas needed to back up my prediction and the shop keeper's statement this was another reason why this investigation went good because I found out the right information needed. If I had the was to investigate even more further to see what results I would get I would make more trays for the rectangles on which I would cut off up to 10.5 or even more half corners I also would make the trays over 24 by 24 and see if I would get the same amount of heights or bigger or smaller, I also would try to use different calculation to see weather or not I get different results. I could try to find out different formulas to use for the algebra and see weather it gave me the same results as the algebra formulas that I used now another thing that I could use is make a decimal line graph, the last thing that I would if I did further investigation is that I would ask for more help and look at different guidance sheets I also would instead of using 1cm squared paper to cut off the halves of the rectangle corners I would use half cm squared paper to get more accurate results. ?? ?? ?? ?? 11.5 ...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 Fencing Problem 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 Fencing Problem essays

  1. A length of guttering is made from a rectangular sheet of plastic, 20cm wide. ...

    =2*D14+10 =F14+B14 =G14/2 =H14*E14 22 10 5 =5*SIN(RADIANS(A15)) =5*COS(RADIANS(A15)) =2*D15+10 =F15+B15 =G15/2 =H15*E15 23 10 5 =5*SIN(RADIANS(A16)) =5*COS(RADIANS(A16)) =2*D16+10 =F16+B16 =G16/2 =H16*E16 24 10 5 =5*SIN(RADIANS(A17)) =5*COS(RADIANS(A17)) =2*D17+10 =F17+B17 =G17/2 =H17*E17 25 10 5 =5*SIN(RADIANS(A18)) =5*COS(RADIANS(A18)) =2*D18+10 =F18+B18 =G18/2 =H18*E18 26 10 5 =5*SIN(RADIANS(A19))

  2. Geography Investigation: Residential Areas

    possible for a theorem to help us understand the way our towns and cities we live in are growing? Well personally I think no, and so I have set myself the challenge to investigate Basingstoke's residential areas and conclude with, if Basingstoke doesn't fit into any of the other models

  1. Biological Individual Investigation What Effects Have Management Had On Grasses In Rushey Plain, Epping ...

    (0.07, 1.62) (7.43, 0.91) (1.01, 3.43) (8.91, 4.93) (3.57, 2.12) (8.82, 2.88) (6.31, 5.17) Ground Cover (%) Bare Ground 2 Leaf Litter 6 3 12 14 23 11 Grass 94 8 72 98 100 12 77 48 100 24 Rush 89 16 74 41 76 Bracken Light (lux)

  2. This investigations purpose is to determine which parts of the body are more sensitive ...

    did each body part three times and would have noticed any anomaly very easily. Conclusion From this investigation, I have discovered that the more sensitive area of the body are the ends and tips of limbs, such as the fingertips and the palms of the hands.

  1. Geography As Environmental Investigation

    The readings could be disrupted by other sounds such as talking. Questionnaire To find the first hand opinions of the people that are prevalent in the area. I will present my questionnaire to at least one person on each of the sites.

  2. Arceology paper

    As such, it is important to keep the probes close enough together that they give a good idea of what is below ground while still being able to see a variety of item sizes, but not so close that the large features are missed.

  1. GCSE Physics - Huddling Heat Investigation and Surface Area Coursework

    � � � � � � � � � � � � +,89EFR�����������������������������gd�>�RS_`lmno�����������������������������������������$a$gdX@�$a$gdX@�gd�>����opqr����STUVWX�����������������gd�>�$a$gdX@�$a$gdX@�&1�h:p�>���/ ��=!�'"�'#��$��%��D@�D NormalCJ_H aJmH nHsH tHDA@�D

  2. Regeneration has had a positive impact on the Sutton Harbour area - its environment, ...

    Again, I will tally the results to my questionnaire that has been designed to find out what local people and visitors think of the regeneration of Sutton Harbour, and what they think the most successful parts of it are at the moment.

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