Maths Coursework : Tubes

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Maths Coursework : Tubes

Syllabus 1385

TASK 2

TUBES

The basis of my investigation is, when I fold in various ways a piece of card like this, what will occur.

32cm

24cm

These are the prisms I will be using:

The first shape I will try to investigate will be rectangles. I will try all the various possibilities. I will start on the smaller side i.e. the 24cm. A substantial rule to remember to find the volume, is Length x Height x Width.

A = 11 x 1 = 11

V = 11 x 32 = 352cm(

A = 10 x 2 = 20

V = 20 x 32 = 640cm(

A = 9 x 3 = 27

V = 27 x 32 = 864cm(

A = 8 x 4 = 32

V = 32 x 32 = 1024cm(

A = 7 x 5 = 35

V = 35 x 32 = 1120cm(

A = 6 x 6 = 36

V = 36 x 32 = 1152cm(

A = 5 x 7 = 35

V = 35 x 32 = 1120cm(

I realised in this review that the more cubic the piece of card gets the more possibilities in maximising its volume space. To prove this notion I even tried to work out the rectangle after it, which resulted in a smaller volume.

After folding along the 24cm side, I moved on to the 32cm edge, the results are worked out in the same way except that the depth is now 24cm instead of 32cm.

A = 15 x 1 = 15

V = 15 x 24 = 360cm(

A = 14 x 2 = 28

V = 28 x 24 = 672cm(

A = 13 x 3 = 39

V = 39 x 24 = 936cm(

A = 12 x 4 = 48

V = 48 x 24 = 1152cm(

A = 11 x 5 = 55

V = 55 x 24 = 1320cm(

A = 10 x 6 = 60

V = 60 x 24 = 1440cm(

A = 9 x 7 = 63

V = 63 x 24 = 1512cm(

A = 8 x 8 = 64

V = 64 x 24 = 1536cm(

A = 7 x 9 = 63

V = 63 x 24 = 1512cm(

This examination proved my theory again, that squares have the biggest volume. This proves that shapes that are regular have a bigger volume than those that are not regular.

The biggest volume the rectangle ever reached was 1536cm³, to enforce this fact I have drawn a table:

24cm length

Length

x

Width

x

Depth

=

Volume

X

1

X

32

=

352cm(

2

X

0

X

32

=

640cm(

3

X

9

X

32

=

864cm(

4

X

8

X

32

=

024cm(

5

X

7

X

32

=

120cm(

6

X

6

X

32

=

152cm(

7

X

5

X

32

=

120cm(

8

X

4

X

32

=

024cm(

9

X

3

X

32

=

864cm(

0

X

2

X

32

=

640cm(

1

X

X

32

=

352cm(

32cm side

Length

x

Width

x

Depth

=

Volume

X

5

X

24

=

360cm(

2

X

4

X

24

=

672cm(

3

X

3

X

24

=

936cm(

4

X

2

X

24

=

152cm(

5

X

1

X

24

=

320cm(

6

X

0

X

24

=

440cm(

7

X

9

X

24

=

512cm(

8

X

8

X

24

=

536cm(

9

X

7

X

24

=

512cm(

0

X

6

X

24

=

440cm(

1

X

5

X

24

=

320cm(

2

X

4

X

24

=

152cm(

3

X

3

X

24

=

936cm(

4

X

2

X

24

=

672cm(

5

X

X

24

=

360cm(

I would like to move on to triangles, and determine what their biggest volume would be. To work out the area of a triangle the formulae needed is half base times height. In this particular case I am not given the height, so foremost I have to work out the height, this is done using what's known as Pythagerous's Theorem. This method used is, A² + B² = C ².

A is known as the base, B the height, and C the length. But in this specific case the formulae is rearranged to C² + A² = B² .

As a matter of interest another way to work out the area of a triangle is (AB Sin C, but this only works when the triangle is when you know 2 sides and the angle between them.

The triangles I will be investigating are only isosceles, as any other kind would take too long, and it makes the calculations easier.
Join now!


Here again, once the area of the triangle is found like last time you have to times the area by the length of the prism to find the volume.

I will start with triangles folded on the 24cm side:

1 11

B = 11( - 1( = 121 - 1 = 120

B = 120 = 10.95

Area = 10.95 x 1 = 10.95cm(

Volume = 10.95 x 32 = 350.54cm(

2

B = 10( - 2( = 100 - 4 10 B = 96 = 9.8

Area ...

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