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

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SUMMARY

The discussion focuses on the methods used to calculate the volume of irregularly shaped drinking bottles and containers, such as those produced by Coca-Cola. Key techniques mentioned include volume integrals, both analytic and numerical, as well as experimental methods involving filling the container with a known volume of liquid. The importance of calculus and analysis in these calculations is emphasized, particularly in relation to designing bottles that accurately hold specified volumes like 250 ml.

PREREQUISITES
  • Understanding of volume integrals in calculus
  • Familiarity with numerical approximation techniques
  • Basic knowledge of experimental measurement methods
  • Experience with computer-aided design (CAD) software for bottle modeling
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  • Research "Volume Integral Calculus" for a deeper understanding of the mathematical principles
  • Explore "Numerical Methods for Volume Calculation" to learn about grid-based approximation techniques
  • Study "Experimental Methods in Volume Measurement" to understand practical approaches
  • Learn about "CAD Software for Product Design" to see how volume calculations are integrated into design processes
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Manufacturing engineers, product designers, and anyone involved in the design and production of beverage containers will benefit from this discussion, particularly those looking to improve accuracy in volume calculations.

kweba
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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.
 
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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.
 
mfb said:
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.

mfb said:
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.
 
kweba said:
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.
 

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