How to calculate/find the volume of drinking bottles and product containers?

[kweba]

I'm not sure if this is the right forum category to post this, but I'm pretty sure this still has something to do with geometry. So I apologize in advance.

Looking at soda/juice bottles, water containers, and even drinking cans has always make me wonder how do they (the manufacturing/bottling companies) exactly calculate the exact volume of their containers - which are considerably irregular in shapes that even have curves. The Coca-Cola bottle itself is known for its "sexy" form because of its curvature in the middle (more or less). So how can they say it's exactly "250 ml" in their bottles/containers, for example? What kind of math and engineering techniques do they use, to calculate and make these bottles?


Thank you.

 

[mfb]

If you have analytic expressions for the boundary: A volume integral.
If you have some numerical approximation: A numerical volume integral (a very simple method is "use some grid, count the number of grid points inside")
Or, the experimental method: Take 250ml, fill it into the bottle.

 

[kweba]

If you have analytic expressions for the boundary: A volume integral.
If you have some numerical approximation: A numerical volume integral (a very simple method is "use some grid, count the number of grid points inside")

Volume Integral. I knew it has something to do with Calculus/Analysis! Although I'm not still familiar with such mathematics. So I don't really unserstand how would that method go.

Or, the experimental method: Take 250ml, fill it into the bottle.

And then adjust the bottle's size/scale/shape, enough to fit the 250ml? Sorry if I don't make sense.

 

[mfb]

Volume Integral. I knew it has something to do with Calculus/Analysis! Although I'm not still familiar with such mathematics. So I don't really unserstand how would that method go.

For an introduction to volume integrals, check some book. For a very quick overview, see the wikipedia article

And then adjust the bottle's size/scale/shape, enough to fit the 250ml? Sorry if I don't make sense.

Well, it would be possible ;), but designing bottles at the computer and calculating their volume there is more practical.