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• Level: GCSE
• Subject: Maths
• Word count: 2919

# A length of guttering is made from a rectangular sheet of plastic, 20cm wide. What is the best position for the folds so that the guttering carries the maximum amount of water?

Extracts from this document...

Introduction

Guttering Coursework

Question

A length of guttering is made from a rectangular sheet of plastic, 20cm wide. What is the best position for the folds so that the guttering carries the maximum amount of water?

1st Method

To find out the best place to fold two flaps on the 20cm sheet to find the best area. To do this we used trial and improvement so we went from 0 to 20 increasing the height by 2cm till we found the best area which was 10cm by 5cm we put the values into a table and then plotted a graph.

 Width(cm) Height(cm) Area(cm²) 20 0 0 18 1 18 16 2 32 14 3 42 12 4 48 10 5 50 8 6 48 6 7 42 4 8 32 2 9 18 0 20 0

We then did it for a 30 cm sheet

 Width(cm) Height(cm) Area(cm²) 30 0 0 28 1 28 26 2 52 24 3 72 22 4 88 20 5 100 18 6 108 16 7 112 15 7.5 112.5 14 8 112 12 9 108 10 10 100 8 11 88 6 12 72 4 13 52 2 14 28 0 30 0

We then tried to find a formulae that will find any area with x as the value this is what we found

X/4

X/2

 Angle Base Side X Y A A+B A+B/2 A+B/2*Y 0 10 5 0 5 10 20 10 50 10 10 5 0.868241 4.924038765 11.73648 21.73648 10.86824 53.51564 20 10 5 1.710101 4.698463104 13.4202 23.4202 11.7101 55.01948 30 10 5 2.5 4.330127019 15 25 12.5 54.12659 40 10 5 3.213938 3.830222216 16.42788 26.42788 13.21394 50.61232 50 10 5 3.830222 3.213938048 17.66044 27.66044 13.83022 44.44948 60 10 5 4.330127 2.5 18.66025 28.66025 14.33013 35.82532 70 10 5 4.698463 1.710100717 19.39693 29.39693 14.69846 25.13585 80 10 5 4.924039 0.868240888 19.84808 29.84808 14.92404 12.95766 90 10 5 5 3.06287E-16 20 30 15 4.59E-15 21 10 5 1.79184 4.667902132 13.58368 23.58368 11.79184 55.04315 22 10 5 1.873033 4.635919273 13.74607 23.74607 11.87303 55.04242 23 10 5 1.953656 4.602524267 13.90731 23.90731 11.95366 55.01699 24 10 5 2.033683 4.567727288 14.06737 24.06737 12.03368 54.96658 25 10 5 2.113091 4.531538935 14.22618 24.22618 12.11309 54.89094 26 10 5 2.191856 4.493970231 14.38371 24.38371 12.19186 54.78984 27 10 5 2.269952 4.455032621 14.5399 24.5399 12.26995 54.66304 28 10 5 2.347358 4.414737964 14.69472 24.69472 12.34736 54.51035 29 10 5 2.424048 4.373098536 14.8481 24.8481 12.42405 54.33159 21.5 10 5 1.832506 4.65208784 13.66501 23.66501 11.83251 55.04586

2nd Method

We already had the angle the base and the side but we had to find out side x which was the extension at the top and side y which was the height of the triangle. To find side x we had to to use 5*sin*the angle to find y we did 5*cos*the angle. We then had to find one parallel side to do this we did x*2+10 and the 2

Middle

=2*D20+10

=F20+B20

=G20/2

=H20*E20

28

10

5

=2*D21+10

=F21+B21

=G21/2

=H21*E21

29

10

5

=2*D22+10

=F22+B22

=G22/2

=H22*E22

21.5

10

5

=2*D23+10

=F23+B23

=G23/2

=H23*E23

We then did the same but used 15cm as a base hgere are the results:

Conclusion

Angle

Half  Base

Height

Area of 1 Triangle

Total Area

30

4

=A22/B22

=180/(B22*2)

=C22/2

=E22*F22

=G22*B22

30

5

=A23/B23

=180/(B23*2)

=C23/2

=E23*F23

=G23*B23

30

6

=A24/B24

=180/(B24*2)

=C24/2

=E24*F24

=G24*B24

30

7

=A25/B25

=180/(B25*2)

=C25/2

=E25*F25

=G25*B25

30

8

=A26/B26

=180/(B26*2)

=C26/2

=E26*F26

=G26*B26

30

9

=A27/B27

=180/(B27*2)

=C27/2

=E27*F27

=G27*B27

30

10

=A28/B28

=180/(B28*2)

=C28/2

=E28*F28

=G28*B28

30

11

=A29/B29

=180/(B29*2)

=C29/2

=E29*F29

=G29*B29

30

12

=A30/B30

=180/(B30*2)

=C30/2

=E30*F30

=G30*B30

30

13

=A31/B31

=180/(B31*2)

=C31/2

=E31*F31

=G31*B31

30

14

=A32/B32

=180/(B32*2)

=C32/2

=E32*F32

=G32*B32

30

15

=A33/B33

=180/(B33*2)

=C33/2

=E33*F33

=G33*B33

30

16

=A34/B34

=180/(B34*2)

=C34/2

=E34*F34

=G34*B34

30

17

=A35/B35

=180/(B35*2)

=C35/2

=E35*F35

=G35*B35

30

18

=A36/B36

=180/(B36*2)

=C36/2

=E36*F36

=G36*B36

30

19

=A37/B37

=180/(B37*2)

=C37/2

=E37*F37

=G37*B37

30

20

=A38/B38

=180/(B38*2)

=C38/2

=E38*F38

=G38*B38

30

180

=A39/B39

=180/(B39*2)

=C39/2

=E39*F39

=G39*B39

Total (cm)

Number Of Sides (cm)

Length Of Sides (cm)

Angle

Half  Base

Height

Area of 1 Triangle

Total Area

30

4

7.5

22.5

3.75

9.053301

33.94987822

135.7995

30

5

6

18

3

9.233051

27.69915183

138.4958

30

6

5

15

2.5

9.330127

23.32531755

139.9519

30

7

4.285714286

12.85714

2.142857

9.388471

20.11815123

140.8271

30

8

3.75

11.25

1.875

9.426262

17.6742404

141.3939

30

9

3.333333333

10

1.666667

9.452136

15.75356061

141.782

30

10

3

9

1.5

9.470627

14.20594091

142.0594

30

11

2.727272727

8.181818

1.363636

9.484299

12.93313532

142.2645

30

12

2.5

7.5

1.25

9.494693

11.8683658

142.4204

30

13

2.307692308

6.923077

1.153846

9.502778

10.96474387

142.5417

30

14

2.142857143

6.428571

1.071429

9.509192

10.18841955

142.6379

30

15

2

6

1

9.514364

9.514364454

142.7155

30

16

1.875

5.625

0.9375

9.518597

8.923684911

142.779

30

17

1.764705882

5.294118

0.882353

9.522105

8.401857086

142.8316

30

18

1.666666667

5

0.833333

9.525044

7.937536321

142.8757

30

19

1.578947368

4.736842

0.789474

9.52753

7.521734592

142.913

30

20

1.5

4.5

0.75

9.529654

7.147240164

142.9448

30

180

0.166666667

0.5

0.083333

9.549054

0.795754515

143.2358

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