• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month   # A Builder has to make drains from a sheet of plastic measuring 2m x 50cms. He finds the semi-circle produces the best drain. Prove This.

Extracts from this document...

Introduction

PROBLEM:

A Builder has to make drains from a sheet of plastic measuring 2m x 50cms. He finds the semi-circle produces the best drain. Prove This.

INTRODUCTION:

I will hope to prove in this coursework that a semi-circle will make the best drain for a builder. I will show this by calculating the area and volume of the semi-circle and other shapes. Hopefully I will find that the semi-circle will give the best area which will mean that it gives a bigger volume and will therefore hold more.      1.

2.

PROBLEM: Which way would be the best to bend the plastic?

SOLUTION: I would probably choose diagram 2 because it is the longest shape when bent and we would not need as many drains. The reason for me not choosing diagram 1 is because I would need to many pieces of drain to go around the whole house and it would hang to low and look unsightly.

WHICH SHAPES WILL I EXPLORE?

1. Semi-Circle

This Shape is in 2D as if you were looking at it from straight on.

This is how it looks in 3D and how it will look on a building.

1. Rectangle

This is the shape in 2D as if you were looking at it straight on.

...read more.

Middle

25cm

54.265cm

175

25cm

27.136cm

*BOLD indicates turning point.

## Trapezium

By looking at the trapezium I can see that it is made up of two triangles and a rectangle.           We found B as 25cm because when we looked at the findings from the rectangle 25cm gave the best area for our shape.

To find the area for the trapezium I am not going to change the lengths of the side instead I will change the angle θ. The values for the angles can range from 1 to 89. For calculating each of my angle sizes I will go up in steps of 5.

To find the area of the trapezium I will use the formula:

Area of trapezium = ½ the sum of the parallel sides by the

Perpendicular height.                  ## Working Out For Trapezium

To find X we use the equation:

Sin45 = X/12.5

X = 12.5 Sin45 X = 8.8388cms

To find Y we use this equation:

Y = 2X+25

= 2(8.8388)+25

= 42.6776

To find H we use the equation:

Cos45 = H/12.5

H = 12.5 Cos45

H = 8.8388cms

...read more.

Conclusion

Area of test-tube = Area of Semi-circle + area of rectangle

= 366.897 + 15.287

= 382.184

Height of Rectangle (side) cm

Circum. Of semicircle

Cm

Radius of the semicircle

Cm

Area of semicircle

Cm2

Cm

Area

Cm2

Total Area

Cm2

1

15.29

7.645

367.04

30.58

30.58

397.62

2

14.65

7.325

336.96

58.6

117.2

454.16

4

13.38

6.69

281.07

107.04

428.16

709.23

6

12.10

6.05

229.86

145.2

871.2

1101.06

8

10.83

5.415

184.14

173.28

1386.24

1570.38

10

9.55

4.775

143.19

191

1910

2053.19

12

8.28

4.14

107.64

198.72

2384.64

2492.28

14

7.01

3.505

77.15

196.28

2747.92

2825.07

16

5.73

2.865

51.55

183.36

2933.76

2985.31

18

4.46

2.23

31.23

160.56

2890.08

2921.31

20

3.18

1.59

15.88

127.2

2544

2559.88

22

1.91

0.955

5.73

84.04

1848.88

1854.61

24

0.64

0.32

0.64

30.72

737.28

737.92

## Conclusion

Now that I have investigated all five shapes I can now display my findings in order in the table below. The shapes are listed from the one with the largest area/volume to the one with the smallest. The one with the largest area/volume is the best shape for a drain.

###### Stage

Area

1

392.5

5

382.184

2

312

4

299.09

3

289.389

I can now see that the best drain is the semi-circle as it has the greatest area and volume.

## Extension

If I had more time I would have been able to investigate after shapes and went on to investigate about different sizes of plastic and how they effect the area and volume of the drain.

Evaluation

I found this project very rewarding and I thoroughly enjoyed it. I was pleased when at the end I found that the semi-circle was the shape that gave the greatest area and volume.

Although I enjoyed most of the project I found some parts quite difficult, for example the area of the trapezium had a lot of complex working out to do.

There are parts of the project that I could have made more accurate by rounding to a higher decimal place or using the Π button on the calculator.

...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

# Related GCSE Fencing Problem essays

1. ## A length of guttering is made from a rectangular sheet of plastic, 20cm wide. ...

=2*D4+10 =F4+B4 =G4/2 =H4*E4 10 10 5 =5*SIN(RADIANS(A5)) =5*COS(RADIANS(A5)) =2*D5+10 =F5+B5 =G5/2 =H5*E5 20 10 5 =5*SIN(RADIANS(A6)) =5*COS(RADIANS(A6)) =2*D6+10 =F6+B6 =G6/2 =H6*E6 30 10 5 =5*SIN(RADIANS(A7)) =5*COS(RADIANS(A7)) =2*D7+10 =F7+B7 =G7/2 =H7*E7 40 10 5 =5*SIN(RADIANS(A8)) =5*COS(RADIANS(A8)) =2*D8+10 =F8+B8 =G8/2 =H8*E8 50 10 5 =5*SIN(RADIANS(A9))

2. ## The best shape of guttering

24 400 18 3 21600 54 400 24 400 16 4 25600 64 400 24 400 14 5 28000 70 400 24 400 12 6 28800 72 400 24 400 10 7

1. ## Fencing problem.

radius the subject. This has been shown below: Radius = 1000 � 2? Radius = 1000 � 6.283185307 Radius = 159.1549431 I shall now substitute the value that was found of the radius into the formula to find the area of the circle: Area of a circle = ?

2. ## The Fencing Problem

Area = 4 (.5 ( (1000 ( 4)) ( ((500 ( 4) ( (tan (180 ( 4)) = 62,500m� This is correct. Regular Pentagon: The area of a regular pentagon with a perimeter of 1000m is Area = (.5 ( 200 ( 137.638)

1. ## The Fencing Problem

As a result, I will now analyse rectangles in the next stage of my investigation. Quadrilaterals - Rectangles I will proceed to show the maximum possible area for a rectangle with perimeter = 1000m; again, presenting my results in a graph.

2. ## Regeneration has had a positive impact on the Sutton Harbour area - its environment, ...

From this we would know if the area was attracting the most number of people by various different methods. If it was not well signposted, the area potentially wasn't attracting the full amount of people that it could do. Question 5- "Why are you here?"

1. ## Based on the development of the BristolHarbourside the title that I chosen for my ...

There were three problems related to the questionnaires. The first was how we decided who to ask. Would I, if a group of fifty people were walking past, ask the first, second and third person to complete our questionnaire or another order of people. In I decided to ask the first people who walked past this was because

2. ## A group of researchers set up a series of observation sites in the Arctic ...

With angles such as 30 degrees a mirror line could be used in the y = -x axis to find the resultants flying back in the opposite direction. Symmetry in the y-axis would get you the opposites of that angle in which the two triangles are drawn together side by side as shown in my scale drawings for 45-degrees. • Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to
improve your own work 