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

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Discussion Overview

The discussion revolves around the methods used to calculate the volume of irregularly shaped drinking bottles and product containers, touching on aspects of geometry, calculus, and practical manufacturing techniques.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses curiosity about how manufacturers determine the volume of containers with irregular shapes, such as soda bottles, and questions the mathematical and engineering techniques involved.
  • Another participant suggests using analytic expressions for the boundary to perform a volume integral, or alternatively, employing numerical methods such as counting grid points within the shape.
  • A different participant reiterates the idea of using volume integrals and expresses a lack of familiarity with the mathematics involved, questioning how to apply these methods practically.
  • Some participants mention the experimental method of filling a container with a known volume (e.g., 250 ml) to verify capacity, while also discussing the potential for adjusting the bottle's design to fit a specified volume.
  • There is a suggestion that designing bottles using computer software for volume calculations may be more practical than manual methods.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a single method for calculating volume, as multiple approaches are discussed, including analytical, numerical, and experimental methods. Uncertainty remains regarding the application of these methods, particularly for those less familiar with calculus.

Contextual Notes

Some participants express limitations in their understanding of calculus and volume integrals, indicating a need for further clarification or resources to grasp these concepts fully.

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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