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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

image00.png

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

image01.png

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

...read more.

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

image02.png

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

...read more.

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

image05.png

...read more.

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