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Investigation Task Essay Example
 Category:Mathematics
 Document type:Math Problem
 Level:High School
 Page:1
 Words:288
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Capacity of cylindrical can is 450 mls=450cm3
450= πr^{2}h
h=450/ πr^{2}
Surface area of closed cylindrical can, S=2πr2 + 2πrh
Therefore, S=2πr^{2} + 2πr450/ πr^{2;} this is simplified to, S=2πr^{2} + 900/ r
^{}S=2πr^{2} + πr900/ πr^{2}; taking S to be Y and r to be X; the
The equation becomes y=2πx2 + 900/ x
Table of radius and surface area is shown below
The graph appears as shown in Chart 1 below

The minimum point is shown where the graph make a turn, where X=4, and y=325.5
Using h=450/ πr^{2 }where r, is 4cm,
h=450/ π (4)^{2}
h=450/3.14(16) = 450/50.24=8.96cm
Other 8 cans:
When x =1; h=450/ 3.14 (1)^{2 }=143.31 cm
X=2; h=450/ 3.14 (2)^{2} =35.83 cm
X=3; h=450/ 3.14 (3)^{2}=15.92 cm
X=5; h=450/ 3.14 (5)^{2} =5.73 cm
X=6; h=450/ 3.14 (6)^{2} =3.97cm
X=7; h=450/ 3.14 (7)^{2} =2.92 cm
X=8; h=450/ 3.14 (8)^{2} =2.24 cm

The surface area is as shown in the table 1 above.

The recommended can is the one that gives us the minimum S.A. holding the same capacity of 450 ml which is can r=4cm, h=8.96cm and S.A. =325.5 cm^{2}
Cylindrical models, are good absorbers of shock, good storage for fluid related substance, providing much pouring ease. One main disadvantage is that they leave a lot of space between one another unlike cubes.
A cube can is ease to manufacture, due to its straightforward creases and folds. Very little material goes to waste during manufacturing and most of the material wasted can be recycled. Also, setting up the required materials and equipment is usually cheap unlike complex nets (Groth, 34).
d). Scale drawing
Works cited
Growth, Chuck. “The Art and Techniques of Designing Exceptional Packaging.” Delmar Cengage Learning. 2006. Print.