Volume of a barrel.

[Tugdual]

(03-21-2016 07:44 AM)ggauny@live.fr Wrote:  Hi,
My question is how exactely find the exact capacity of a barrel and why it is not a unique answer, and why so many equations ?
Me I dont' know what is parabola or eliptic curve, so for my excercise to do for
I encounter problems of course.
Dieter was speaking of Kepler, so I had remember in my "very" old book of geometrie, when I was in school before go to work there is a solution without complicated formulas.
I will do my excercise like in this time.

A cylinder is a barrel with flat sides but immediately you suspect it cannot have the same volume as a wine barrel. And here is the answer to your question: there is no such thing as a unique barrel, hence there are multiple answers.
https://fr.m.wikipedia.org/wiki/Tonneau_(formules)
The generic way to calculate the volume of a barrel is to cut it into a stack for extremely thin slices, so thin that you might consider that each slice is a cylinder. You then sum the volume of each cylinder to achieve the entire barrel volume. A thin cylinder height is called dx (where x is travelling on the vertical axis of the cylinder) and the summing operation is called an integration. Solving the problem is as simple as resolving an integral equation.

Remember that when attending math class, the current lesson is giving you clues about how to solve the problem. Are you learning integral equations?