This is an illustration of the different types of cans that can be used. The problem calls for the production of a can that can hold 40 cubic inches of juice. The can produced can be short and wide, or tall and narrow. The can will have a relationship between the radius and height. The radius will be large when the height is small or the radius will be small when the height is large.
This table shows the amount of material, M, used in the can for various choices of radius, r, and height, h.
It shows that the amount of material is greatest at the extremes values of radius and height. The table also shows that the optimal length of radius is somewhere in the interval [1.0, 3.0].
|
r (in) |
h (in) |
M (inē) |
|
0.2 |
318.31 |
400.25 |
|
1.0 |
12.73 |
86.27 |
|
2.0 |
3.18 |
65.09 |
|
3.0 |
1.41 |
83.13 |
|
4.0 |
0.80 |
120.64 |
|
10.0 |
0.13 |
636.49 |