Standard soft drink cans hold 12 ounce or 355 milliliters of soda. Assume that soda can must be right circular cylinders. Through trial and error with cans of different sizes, find the dimensions of a 12-ounce can that has the lowest cost for materials.

Answer 1

π r^2 h = 355
r^2 h = 113
the area a=2πrh+2πr^2 which we want to be small
113 is prime, so there will not be integer values. However, using integers to approximate,

r h a/2π(r^2+rh)
3 13 48
4 7 44
5 4 45
6 3 54
Looks like r is near 4