• Category:
Mathematics
• Document type:
Math Problem
• Level:
High School
• Page:
1
• Words:
288

Submission date:

1. Capacity of cylindrical can is 450 mls=450cm3

450= πr2h

h=450/ πr2

Surface area of closed cylindrical can, S=2πr2 + 2πrh

Therefore, S=2πr2 + 2πr450/ πr2; this is simplified to, S=2πr2 + 900/ r

S=2πr2 + πr900/ πr2; 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

1. The minimum point is shown where the graph make a turn, where X=4, and y=325.5

Using h=450/ πr2 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

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

2. 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 cm2

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.