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Comparing the surface area of different shapes with the same volume

Extracts from this document...

Introduction

What shape container should we use?

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March 27th, 2010

Class of 9ic1

Cris Strat

Table of Contents

1. Title page

2. Table of contents

3. Introduction to project

Main body

4. Procedures, methods, results

4.1 Analysis of results

5. Conclusion

6. Bibliography

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3.

Introduction

The class of 9ic1, lead by mathematician Paul Chodak, was given an end of epoch task/project to complete. The project that was given to us entailed the completion of a container surface area comparison, when having two containers with the same exact volume. The respective students were needed to utilize algebraic expressions, to understand the problem that was asked of them and to conclusively decide which of the two containers should be used, to create and produce the cheapest container for the Blackwood Potato Chip Company. This project, is seemingly very easy to complete, however it requires strenuous work to complete a computer generated presentation and case result. The students are given 2 weeks to complete the project and have at least two lessons in class to start and possibly complete the project.

...read more.

Middle

πr2 x h

h= 1000cm3/πr2

Surface Area of Cylinder with imputed h

Abpcc = πr2 + 2πrh

Abpcc = πr2 + 2πr (1000cm3/πr2)

B)

1000cm3= a2 x H

H= 1000cm3/ a2

Surface Area of Rectangular prism with imputedH

Abpcc= a2+ 4aH

Abpcc= a2+ 4a(1000cm3/ a2)

  1. Then a complete table for both the cylinder and the prism must be done. The table must include the standard base length, base area, height and surface area

The cylinder

Radius, r

4.00

5.00

6.00

7.00

8.00

9.00

10.0

11.0

12.0

Base area, πr2

50.3

78.5

113

154

201

254

314

380

452

Height, h

19.9

12.7

8.84

6.50

4.97

3.93

3.18

2.63

2.21

Surface Area

550

479

446

440

451

477

514

562

619

The rectangular prism

Radius, r

4.00

5.00

6.00

7.00

8.00

9.00

10.0

11.0

12.0

Base area, a2

16

25

36

49

64

81

100

121

144

Height, H

62.5

40.0

27.8

20.4

15.6

12.3

10.0

8.26

6.94

Surface Area

1016

825

703

620

564

525

500

485

477

...read more.

Conclusion

2 less material, which means that the production costs are smaller for the company and with that in mind higher profits also.

5. Conclusion

In conclusion, the Blackwood Potato Chip Company should use the cylinder, as the new shape for packaging. The cylinder will be much cheaper to produce and at the same time also a lot easier to produce. Even though the difference is not huge, every cent given to charity helps. For the BPCC and their consumers, when it is possible to create something at a smaller cost, more environmentally safe and at the same time also help a charity, of course the company and the consumer will pick that choice.

Yet, again I must re- state the fun and the knowledge I have, after doing this project. At, first it seemed as it was going to be impossible to do. This is a conclusion to which many of us jump immediately, it is easy to give up from the start however, we must all keep one saying in mind “never say never” because if you put your mind to it, the impossible becomes possible.

...read more.

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