Is the 12 oz soda can the best design?

[stacytrace]

Is the 12 oz soda can the best design? :?: :?:

Hint: Minimize the surface area. The total surface area is the sum of the area of two circles forming the can's ends and the lateral area of the cylinder forming the can's sides.

 

[stapel]

Define "best". What considerations are in play? Are we minimizing input materials? Are we then taking thickness-versus-pressure into account? Are we thinking at all about ergonomics, or does it not matter that a too-wide can might not fit comfortably into the human hand? Do we care if every vending machine has to be re-engineered to fit our new can design, or that we'll simply lose all of those sales?

Note: The bottom end of the can is not a simple circle. Being unreinforced (the lid is made of sterner stuff), the pressure of the contents is counteracted by the parabolic shape of the base. Are we not to take that into account?

Please reply with the rest of the specifications, along with the definition of "best". When you reply, please include all of your work and reasoning so far. Thank you.

Eliz.

 

[stacytrace]

Well.....

This what I have so far:
Surface: 2(3.14)(r^2)+2(3.14)(r)(h)

Volume: 2(3.14r^2)(h)=355 ml or cm^3
h=355/2(3.14)(r^2)

12oz is not a volume measure


s(r)=2(3.14)(r^2)+2(3.14)(r)(355/2(3.14)(r^2)
s(r)=2(3.14)(r^2)=355/r
s'(r)=
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[stapel]

12oz is not a volume measure

"Fluid ounces" is indeed a measure of volume.

Meanwhile, what is meant by "best"? And are we supposed to work only with the simplified shape (with the flat bottom), or the real-world shape? And should we consider wall-thickness and the pressure of carbonation?

Thank you.

Eliz.