Calculating sizes on teaware

[Pouvla]

On alot of online sites, they only list the height and diameter of the cups and thus some calculating is needed to figure out how much tea it can hold.

It being a while since I attended math classes I forgotten all about calculating the size based on just height and diameter but I found V = π·r^2*h should do the trick..

I pop in the numbers on google calc but I get some non-matching results..
For instance I tested with This cup from artisticnippon which they say is 300ml to the rim (yes I operate in the proper measurements, the metrics) but pi * (4,6^2) * 8,3 = 551,751635,
so is the formula the wrong one, is artisticnippon not the best with the measures (do they perhaps measure the diameter in the top of the cups, which could be a problem for yunomis), does the clay of the cup take up the 251 extra ml that the formula shows?

Or it is simply safer to email them for each cup I might be interested in and ask for a size? this isnt just for artisticnippon, alot of sites dont give up the ml/oz sizes for cups which is quite nessecary imo..

[TomVerlain]

the cup is not really a cylinder. The diameter at the top is very different from the diameter at the bottom. It is more of a "conic section". As you point out, those are outside measurements, so inside would be less as well.

It might be easier to guesstimate the volume by shopping for cups of the aproximate height and width of cups you know, that have the volume you like, or just email. Since most people do not fill cup to the absolute top, even 300 ml for that would be more than you would actually want to have in the cup.

[JBaymore]

For most cups, you are looking at calculus to figure the volume inside the complex curves.

You can approximate it by breaking it down into easy to calculate solid geometric shapes like cylinders, truncated cones, and so on and then adding the volumes of the various segments together.

best,

.................john

[MarshalN]

Yeah, you need to integrate to get the right answers. Unless the cup is a straight up cylinder or some other regular shape (unlikely) you won't get the right answer.

[Dresden]

Remember that 1 cubic centimeter = 1ml

Make sure all your numbers are in terms of centimeters.

You won't get an exact answer without calculus but you can probably get a close enough approximation for your needs.

[betta]

Not really worth it to calculate the volume mathematically. With those wavy shape, you must build the inclined sinusoidal function of the curvature, integrate it along the height of the cup, times the outer circumference. And then deduct this value from a cylinder volume with diameter equal to diameter of the brim.
This all only get you an approximate volume, not yet including additional correction due to volume occupied by the material.
In brief, ask Toru-san to measure it for you more accurately by measuring weight of water required to fill the cup fully. Then you can calculate the volume as 1 g water approximately equal to 1 mL .
So far I am very satisfied with everything from Artisticnippon, including also the item description.