4
Procedures, materials and methods
Materials
For the completion of this project there are some necessary materials that every student or pupil wanting to complete this project must have:
- GDC (Graph Display Calculator)
- “Graph” (www.padowan.dk) or “Grapher” (Apple Applications)
- Areas of interaction sheet with instructions and procedures
Procedures and methods
Even though it is important to have the items mentioned above, it is also very important to follow some easy steps that will conclusively help you achieve the correct answer. The steps that need to be completed are:
- The creation, simplification and application of algebraic expressions to be used for the calculation of the different surface areas and volumes.
Volume and surface area of Cylinder
Vc= πr2
Ac= πr2 x 2 + 2πrh
Abpcc = πr2 + 2πrh
Volume and surface area of Rectangular Prism
Vp=a2 x h
Ap= 2a2+ 4a x H
Abpcc= a2+ 4aH
*Bpcc was added to differentiate between the normal surface area of a cylinder and rectangular prism and the formula created for the “Blackwood Potato Chip Company”.
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The use of this algebraic expressions to find h in terms of r for the cylinder and H in terms of a for the prism.
A)
1000cm3= 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 imputed H
Abpcc= a2+ 4aH
Abpcc= a2+ 4a(1000cm3/ a2)
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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
The rectangular prism
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The table has already been formed utilizing Excel as the spreadsheet creation software of choice. All of the numbers mentioned in the chart were rounded to 3 significant figures, through the utilization of the built- in rounding capabilities of Excel. If errors were to occur, the possibility is left to the user, to manually round the numbers to a personal preference of decimal points or figures. For example the second column of both the rectangular prism and cylinder is shown, with all of the decimals points requested by Excel.
2nd Column
Cylinder
Prism
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In the second last step of the project, the use of graphing computer software or a GDC (Graphic Display Calculator) is necessary for the completion of this step. For the most exact answer, the utilization of the GDC was taken as a personal preference. An attempt with Excel’s graphing software was also used; all of the graphs are shown below.
Utilization of GDC (Graphic Display Calculator)
Y= (tab)
Y1= x2+4*x* (1000/x2)
Y2= π*x2+2*π*x*(1000/(π*x2))
TBLSET (Table Set)
Window
Xmin=0
Xmax=20
Xscl=10
Ymin=0
Ymax=1000
Yscl=100
Xres=1
Then to calculate the minimum of both curve lines, the following steps must be followed:
2nd-calc-3: minimum
Left bound-right bound-Guess
*The same steps must be taken for the second line also
Cylinder
Prism
- Then for the last step, required for all those wanting to fully complete the project, is a report which identifies the ‘Best container for mass production’ which has been the center point of this report and the result will also be mentioned and analyzed below.
4.2 Analysis of Results
Below are charts showing the difference between the base areas, heights and surface areas, through the use of charts.
Comparison of base areas
Blue- cylinder and red- prism
Comparison of heights
Blue- cylinder and red- prism
Comparison of surface areas
Blue- cylinder and red- prism
Final Result
The result is that the cylinder has a minimum radius of:
6.8278408
6.83 cm (3SF)
And the minimum radius for the prism is:
12.599207
12.6 cm (3SF)
The minimum surface area for the cylinder is:
439.37757
440 cm2 (3SF)
The minimum surface area for the prism is:
476.22032
476 cm2 (3SF)
Through these results we are able to visibly see that the cylinder is a much better choice for the Blackwood Potato Chip Company as it uses approximately 36 cm2 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.
