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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?

March 27th, 2010

Class of 9ic1

Cris Strat

1. Title page

3. Introduction to project

Main body

4. Procedures, methods, results

4.1 Analysis of results

5. Conclusion

6. Bibliography

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.

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 5 6 7 8 9 10 11 12 Base area, πr2 50.3 78.5 113 154 201 254 314 380 452 Height, h 19.9 12.7 8.84 6.5 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 5 6 7 8 9 10 11 12 Base area, a2 16 25 36 49 64 81 100 121 144 Height, H 62.5 40 27.8 20.4 15.6 12.3 10 8.26 6.94 Surface Area 1016 825 703 620 564 525 500 485 477

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.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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