# 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

=5*SIN(RADIANS(A21))

=5*COS(RADIANS(A21))

=2*D21+10

=F21+B21

=G21/2

=H21*E21

29

10

5

=5*SIN(RADIANS(A22))

=5*COS(RADIANS(A22))

=2*D22+10

=F22+B22

=G22/2

=H22*E22

21.5

10

5

=5*SIN(RADIANS(A23))

=5*COS(RADIANS(A23))

=2*D23+10

=F23+B23

=G23/2

=H23*E23

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

0 | 15 | 7.5 | =5*SIN(RADIANS(A25)) | =5*COS(RADIANS(A25)) | =2*D25+10 | =F25+B25 | =G25/2 | =H25*E25 |

10 | 15 | 7.5 | =5*SIN(RADIANS(A26)) | =5*COS(RADIANS(A26)) | =2*D26+10 | =F26+B26 | =G26/2 | =H26*E26 |

20 | 15 | 7.5 | =5*SIN(RADIANS(A27)) | =5*COS(RADIANS(A27)) | =2*D27+10 | =F27+B27 | =G27/2 | =H27*E27 |

30 | 15 | 7.5 | =5*SIN(RADIANS(A28)) | =5*COS(RADIANS(A28)) | =2*D28+10 | =F28+B28 | =G28/2 | =H28*E28 |

40 | 15 | 7.5 | =5*SIN(RADIANS(A29)) | =5*COS(RADIANS(A29)) | =2*D29+10 | =F29+B29 | =G29/2 | =H29*E29 |

50 | 15 | 7.5 | =5*SIN(RADIANS(A30)) | =5*COS(RADIANS(A30)) | =2*D30+10 | =F30+B30 | =G30/2 | =H30*E30 |

60 | 15 | 7.5 | =5*SIN(RADIANS(A31)) | =5*COS(RADIANS(A31)) | =2*D31+10 | =F31+B31 | =G31/2 | =H31*E31 |

70 | 15 | 7.5 | =5*SIN(RADIANS(A32)) | =5*COS(RADIANS(A32)) | =2*D32+10 | =F32+B32 | =G32/2 | =H32*E32 |

80 | 15 | 7.5 | =5*SIN(RADIANS(A33)) | =5*COS(RADIANS(A33)) | =2*D33+10 | =F33+B33 | =G33/2 | =H33*E33 |

90 | 15 | 7.5 | =5*SIN(RADIANS(A34)) | =5*COS(RADIANS(A34)) | =2*D34+10 | =F34+B34 | =G34/2 | =H34*E34 |

20.5 | 15 | 7.5 | =5*SIN(RADIANS(A35)) | =5*COS(RADIANS(A35)) | =2*D35+10 | =F35+B35 | =G35/2 | =H35*E35 |

21 | 15 | 7.5 | =5*SIN(RADIANS(A36)) | =5*COS(RADIANS(A36)) | =2*D36+10 | =F36+B36 | =G36/2 | =H36*E36 |

21.5 | 15 | 7.5 | =5*SIN(RADIANS(A37)) | =5*COS(RADIANS(A37)) | =2*D37+10 | =F37+B37 | =G37/2 | =H37*E37 |

Angle | Base | Side | X | Y | A | A+B | A+B/2 |

Conclusion

Angle

Half Base

Height

Area of 1 Triangle

Total Area

30

4

=A22/B22

=180/(B22*2)

=C22/2

=E22/TAN(RADIANS(D22))

=E22*F22

=G22*B22

30

5

=A23/B23

=180/(B23*2)

=C23/2

=E23/TAN(RADIANS(D23))

=E23*F23

=G23*B23

30

6

=A24/B24

=180/(B24*2)

=C24/2

=E24/TAN(RADIANS(D24))

=E24*F24

=G24*B24

30

7

=A25/B25

=180/(B25*2)

=C25/2

=E25/TAN(RADIANS(D25))

=E25*F25

=G25*B25

30

8

=A26/B26

=180/(B26*2)

=C26/2

=E26/TAN(RADIANS(D26))

=E26*F26

=G26*B26

30

9

=A27/B27

=180/(B27*2)

=C27/2

=E27/TAN(RADIANS(D27))

=E27*F27

=G27*B27

30

10

=A28/B28

=180/(B28*2)

=C28/2

=E28/TAN(RADIANS(D28))

=E28*F28

=G28*B28

30

11

=A29/B29

=180/(B29*2)

=C29/2

=E29/TAN(RADIANS(D29))

=E29*F29

=G29*B29

30

12

=A30/B30

=180/(B30*2)

=C30/2

=E30/TAN(RADIANS(D30))

=E30*F30

=G30*B30

30

13

=A31/B31

=180/(B31*2)

=C31/2

=E31/TAN(RADIANS(D31))

=E31*F31

=G31*B31

30

14

=A32/B32

=180/(B32*2)

=C32/2

=E32/TAN(RADIANS(D32))

=E32*F32

=G32*B32

30

15

=A33/B33

=180/(B33*2)

=C33/2

=E33/TAN(RADIANS(D33))

=E33*F33

=G33*B33

30

16

=A34/B34

=180/(B34*2)

=C34/2

=E34/TAN(RADIANS(D34))

=E34*F34

=G34*B34

30

17

=A35/B35

=180/(B35*2)

=C35/2

=E35/TAN(RADIANS(D35))

=E35*F35

=G35*B35

30

18

=A36/B36

=180/(B36*2)

=C36/2

=E36/TAN(RADIANS(D36))

=E36*F36

=G36*B36

30

19

=A37/B37

=180/(B37*2)

=C37/2

=E37/TAN(RADIANS(D37))

=E37*F37

=G37*B37

30

20

=A38/B38

=180/(B38*2)

=C38/2

=E38/TAN(RADIANS(D38))

=E38*F38

=G38*B38

30

180

=A39/B39

=180/(B39*2)

=C39/2

=E39/TAN(RADIANS(D39))

=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

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