Using volume as capacity?

JulianMathHelp

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When we have hollow 3D objects such as closed off cans (cylinders), aren’t we technically overestimating the capacity by using the volume? This is because the volume determines how much 3D space the object takes up, and the capacity is how much the object can hold. In the perfect mathmematical word, the volume and capacity would be the same as the faces wouldn’t have thickness, meaning it can hold that much volume, but in the real world, the capacity is slightly less because of the thickness of the faces right?
 
I have a problem which is a can has a radius of 6 inches. Find out how much water can fit in the can.
 
I have a problem which is a can has a radius of 6 inches. Find out how much water can fit in the can.
I would consider the thickness to be 0 in this case.
Yes, an actual can holds less than its volume. But, I'm guessing, soda bottlers use interior volume in their calculations, in case you are referring to numbers on the labels.
 
When we solve problems about capacity of such a can, we just use the inside measurements. which are the actual measurements of the contained liquid. Were you told that the radius was the outside radius, or are you just assuming that?

If an artificial classroom problem you are given doesn't state whether the measurements are inside or outside, just assume they are the measurements you need -- and state your assumption at the start of your work, to let the teacher know that you are aware of the real life issues but also know how to do the work. They are really just assuming negligible thickness for the sake of simplicity.

In a real-life problem, you would make sure you had the appropriate measurements -- either do the inside measurements yourself, or find out the thickness of the walls and subtract that from the radius, and so on.

It is a very old tradition that exercises for students are artificial and simplified, in order to teach the basic concepts without bringing in the complications of real life. It is a good thing that they do this, not a defect! At some point, it will be good to do a real-life problem or two, but it would be very discouraging for students if every problem were that complicated.
 
When we solve problems about capacity of such a can, we just use the inside measurements. which are the actual measurements of the contained liquid. Were you told that the radius was the outside radius, or are you just assuming that?

If an artificial classroom problem you are given doesn't state whether the measurements are inside or outside, just assume they are the measurements you need -- and state your assumption at the start of your work, to let the teacher know that you are aware of the real life issues but also know how to do the work. They are really just assuming negligible thickness for the sake of simplicity.

In a real-life problem, you would make sure you had the appropriate measurements -- either do the inside measurements yourself, or find out the thickness of the walls and subtract that from the radius, and so on.

It is a very old tradition that exercises for students are artificial and simplified, in order to teach the basic concepts without bringing in the complications of real life. It is a good thing that they do this, not a defect! At some point, it will be good to do a real-life problem or two, but it would be very discouraging for students if every problem were that complicated.

Yes, Im pretty sure Teachers don't even pay much attention to the fact of outside and inside radius as us students usually don't even pay attention to the thickness, and think of it to be 0(this really only came to my attention when I was just bored, if I were to receive an actual problem, I probably wouldn't even think about it.)


However, problems like the ones that ask "In attempting to calculate the carrying capacity of a cylindrical pipe, Avery measured the outer diameter to be 2 inches, neglecting to notice that the pipe was one-eighth of an inch thick. By what percent did Avery overestimate the carrying capacity of the pipe?" bring attention to facts like these, and us students will probably notice that.


However, otherwise, I'm pretty sure when problems are trying to ask the carrying capacity of an object, and just state the radius of the circle, they are disregarding the thickness, and making it 0. They also could be referring to the inside radius, though, that seems unlikely as they don't want to complicate it, and it's not really necessary as students don't really think of the thickness of the walls.

Your thoughts on my writing?

-Thanks in advance!
 
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