Math Problem: The Perfect Beer Jug by M0CC4

Last crawled date: 3 years, 4 months ago

This the visulisation of the solution to the "perfect beer jug" math problem.
The math problem
A beer jug should hold 1 liter of beer.
The jug is perfect, if it has the minimal surface area, and therefore using the least amount of material to manifacture.
Simplifing the problem, we assume the jug to only consist of a cylinder wall and a round bottom layer, no handles, no extras.
What is the height and the radius of the perfect beer jug?
How to solve
Find function A(r,h) for the total area of the jug.
Understand the relation between r and h in regards of volume, and remember that 1L = 1dm^3.
Use relation between r and h, to solve for one of them and substitute it in A(r,h).
Now you have A as a function of only one variable.
Derive and solve f' = 0, in order to find local minimum.
(Idealy, also discuss why this is a mimimum, not a maximum, and that its even a global minimum)
With one variable solved, use relation to find the other variable.
Solution
r and h are the same - 68,28mm!
The model can be printed for fun and to demonstrate how user-unfriendly a pure material-oriented approach is. As the walls are only 5mm thick to match the "least material possible" as closely as possible in the real world, consider printing with a high fill density%, like 30-60%. Make sure to print walls and tops on the thicker, stronger side as well, as you don't want leaks and waste your fine drink.
Other than that the print is unsurprisingly simple.
I should point out, that most 3D prints do not meet criteria to be considered "food safe".
Do at your own risk - Prost! ;)
Every donation goes to my students and to give them material to work with. No money is spent on beer, only if you explicitly encourage me :P So thanks in advance.