• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 1375

Tubes Maths Investigation

Extracts from this document...

Introduction

TUBES

INVESTIGATION

image00.png

BE HAPPY.

By

LEE SUMMERS

Tubes Investigation

The aim of this investigation is to make tubes out of a piece of paper 24cm by 32 cm.  The tubes have no top or bottom face and the main aim is to work out which shape of tube gives the best volume.  

The first shape I will use to make a tube will be a square base.  This is because it’s an easy shape to start off with.  To work out the volume of the tube I must first work out the area of the base, then multiply this by the height of the tube.  The first tube will have the 24cm side of the paper as the base and 32cm as the height, whilst the second will have the 32cm side as the base and the 24cm side as the height.  Both of these are shown below:  

V=bxh

   =32(6x6)

   =32x36V=volume of tube        

   =1152cm3b=area of base

h=height of tube

V=bxh

   =24(8x8)

   =24x64

   =1536cm3

From this I can see that although the paper from which the tubes are made is the same there is a difference in the volumes, with the larger base giving the largest volume.

...read more.

Middle

x is needed.  To work this out we need to use the length and angle we know and trigonometry.  This stage is shown below

x=tan54x2.4

  =3.30(2d.p.)

The final stage is working out the area of the base.  This can now be worked out easily by using what was found in the last stage.  The height of the triangle is now simply multiplied by the base of the small triangle and the answer is multiplied by the number of sides.  So this is

V=(bxh)

   =32(5(2.4x3.3))

   =32(5x7.92)

   =32x39.64

   =1268.47cm3

The 32cm pentagonal base would, therefore be worked out as:

x=tan54x3.2

  =4.40(2d.p.)

V=(bxh)

   =24(5(3.2x4.4))

   =24(5x14.09)

   =24x70.47

   =1691.30cm3

I shall now use this method to work out the volume of hexagonal tubes, then octagonal tubes.  

24cm hexagonal based tube.  

a=180(6-2)

   =180x4

   =720°

x=tan60x2

  =3.46(2d.p.)

V=n (bxh)

   =32(6(2x3.46))

   =32(6x6.93)

   =32x41.57

   =1330.22cm3

32cm hexagonal based tube

a=180(6-2)

   =180x4

   =720°

x=tan60x2.6

  =4.62(2d.p.)

V=n (bxh)

   =24(6(2.6x4.62))

   =24(6x12.32)

   =24x73.90

   =1773.62cm3

24cm based octagonal tube

a=180(8-2)

   =180x6

   =1080°

x=tan67.5x1.5

  =3.62(2d.p.)

V=n (bxh)

   =32(8(1.5x3.62))

   =32(8x5.43)

   =32x43.46

   =1390.59cm3

32cm based octagonal tube

a=180(8-2)

   =180x6

   =1080°

x=tan67.5x2

  =4.83(2d.p.)

V=n (bxh)

   =24(8(2x4.83))

   =24(8x9.66)

   =24

...read more.

Conclusion

I will set the value for A and modify the value of x to see what shape paper gives the most effivient tube.  

The first value I will try as A will be 100.  This is because it is an easy number to divide and multiply.  I will start off with x being small and gradually make it larger until I think I have found the optimum size for the paper, and as cylinders are the best tube I will use this as a starting point.  The results for this are shown in the table below.  

NOTE:x is equal to l and A/x is equal to h

image01.png

From this table I can see that as the length of the base of the tube increases, so does the volume.  More importantly however is the fact that there appears to be no limit to this and the volume will continue to rise until the paper the tube is made from is the shortest and longest it can possibly be.  

Therefore in order to make a tube with the largest volume it should have the following properties

  • It should have a circular base
  • The base should be very long and the height should be small
  • If the base cannot be circular then it should be a regular polygon with as many sides as possible  

...read more.

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. Fencing investigation.

    2002 = 1002 + x2 2002 - 1002 = x2 30000 = x2 V30000 = x 173.205m = x Now that the perpendicular height of the trapezium has been solved, working out the area is an easy procedure. Area = 1/2 (base + top)

  2. Mathematics Gcse Coursework Tubes Investigation

    � 32 = 1152cm3 Triangular Prism Base � Height = Cross Section � 2 � height of tube. 24 � 3 = 8cm length of one side 8 � 2 = 4cm half on one side 4square + b square = 8square 64 - 16 = b square b square

  1. Perimeter Investigation

    The area of the circle will be ? * r� where r is the radius and 2 * ? * r will be the circumference or perimeter. 2 * ? * r = 1000 r = 1000 = 159.15 2 ? Area = ? * r� = 79572.5 Shape Length of each Side/m Area/m� Equilateral Triangle 325 47932.5

  2. Geography Investigation: Residential Areas

    For instance, if the area has a bad smell then it will receive a higher number out of 15 compared to a place that has no offensive smells. I will then be able to use the total penalty point number and plot it on graphs etc to find if there is a correlation.

  1. GCSE Maths Coursework Growing Shapes

    Pattern no. (n) Width Width - 2n 1 1 -1 2 3 -1 3 5 -1 4 7 -1 5 9 -1 The formula for working out the width of the shape = 2n-1 Check Width = 2n-1 = 2�3 - 1 = 5 Growing Shapes Extension: Pentagons The pattern

  2. Fencing - maths coursework

    (Not drawn to scale) Here is a heptagon that I am going to use as an example. 1000m n 'n' being the number of sides. In this case it will be '7' 360� n As it is a regular polygon so there would be 'n' number of triangles.

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

    Controls and Variables Throughout the experiment, I will try to keep as many of the factors the same, apart from those, which I am comparing. Temperature should be very similar between the two sites, as they are within 100 meters of one another.

  2. Geography As Environmental Investigation

    Bad Fairly Good Good Excellent 5. What is your usual means of transport in this area ? Car Bus Walk Train Cycle Other 6. Do you Think that the new shopping/cinema complex has had a positive affect on the area.

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