Anybody with any moderatorial aspirations?

So I got a plastic rice measuring cup that is 6.5 cm in height, top diameter at 6.5 cm and bottom diameter at 5.5 cm. How to find its volume in liters or ml?

@SnoopyKid is it a frustum? what is it's shape?

@napstablook its bottom diameter is actually around 5.6 cm or a little bit more. The height and the upper diameter seems to be the same size. Yes, shaped like a frustum cone

@SnoopyKid .brainkart.com/article/Volume-of-frustum-of-a-cone_39426

@napstablook I'm not good at math but I'll try to follow that

Hi All...

Hello @JohnRennie Sir

@123 hi :-)

@SnoopyKid do you know the equation for the volume of a cone?

Direction of displacement gives us the spatial direction in space.

@JohnRennie But what is the meaning of direction of velocity?

Displacement = velocity x time. Yes?

@JohnRennie Yes..

And time is a scalar. It has no direction. So the vector displacement has the same direction as the vector velocity.

@JohnRennie unfortunately no John.

@JohnRennie Yes .. I know this meaning sir. I was confused when using differentiation direction of velocity is tangent to the curve. What is the meaning of this direction.

@SnoopyKid it's one of those equations you just have to remember. It can be derived but the derivation is a bit messy.

I understand direction displacement and velocity is same. Isn't any specific meaning of velocity direction which contain information only about velocity?

@JohnRennie ok I just bring the measuring cup to a bright room and now I can see the measuring numbers on it. The uppermost number is 160 ml, but with the calculation formula I followed from the link I got 700 ml... That is not right, right?

@SnoopyKid give me a moment and I'll draw a diagram:

@SnoopyKid uppermost is 160 ml then don't you already have the volume?

@JohnRennie alright Jon.

@napstablook I just bring it to a bright room and then I realized there are measuring numbers on it. The uppermost number is 160 ml but somehow I don't think the maximum volume isn't exactly at 160ml

*is exactly at 160ml

@SnoopyKid your container is like the difference between two cones i.e. in my diagram take the volume of the larger cone and subtract the volume of the smaller cone and you get the volume of the container.

So if you know the formula for the volume of a cone you can easily calculate the volume of the container.

@JohnRennie how to find the height of the entire cone?

@JohnRennie what is 22/7 in this previous link brainkart.com/article/Volume-of-frustum-of-a-cone_39426

It is at the last solution

@SnoopyKid Well we know that the diameter decreases from 6.5cm to 5.5cm in a distance of 6.5cm i.e. as we move the 6.5cm height of the container the diameter decreases from 6.5cm to 5.5cm. Yes?

@JohnRennie Yes

So the diameter reduces by 1cm for every 6.5cm length of the cone. And the point of the cone is where the diameter is zero i.e. where the diameter has been reduced by 6.5cm. So the total length of the cone is 6.5 x 6.5 = 42.25cm.

Hi everyone, is there a good introductory book on semiconductor physics that you can recommend? There wasnt any mention of semicondutor physics books in the resource recommendation question

@JohnRennie I forget to divide the 6.5 cm diameter by 2 to get the radius. So, the radius become 3.25. Using online cone volume calculator, I got the volume 467.33

Any easy mistake :-)

The volume of a cone is ¹⁄₃πr²h, where r is the radius of the base and h is the height of the cone. For the large cone r = 6.5/2 = 3.25 and h = 42.25 so the volume is 467.33 cm³ as you found.

@JohnRennie I followed the formula from the previous link. I already divide the top and bottom diameters by two so we get the radius. I calculate like this 1/3 x 22/7 x (3.25^2 +(3.25+2.8) + 2.8^2) x 6.5 and the answer is 166.509

The small cone has r = 5.5/2 = 2.75 and the height is 42.25 - 6.5 = 37.75.

Is that correct?

22/7 is an approximation for pi

@SnoopyKid I get the volume of the small cone to be 283.12 cm³, so the volume of the container is 467.33 - 283.12 = 184.21 cm³

@SnoopyKid I guess you're using the formula V = ¹⁄₃πh(r₁² + r₁r₂ + r₂²)

You've done it correctly. The only reason our results differ is that you used 2.8 for the radius of the smaller face when it is actually 2.75.

@JohnRennie I see. Thank you. So, the maximum volume of the 160ml plastic rice measuring cup is actually a little bit more than 160ml :) After that, is it not weird that I tried to pour water from the 160 ml cup to a glass and another 160 ml water from a 1000ml measuring cup to an another glass of the same brand and dimensions as the latter glass, and the water volume is actually not the same? The water from the 160ml measuring cup is actually more than the 160ml water from the 1000ml cup after...

I pour it into the glass

If you have a set of scales to hand you can find the volume by weighing the water. At room temp water weighs one gram per cm³ so 160 cm³ should weigh 160g.

The scales on containers are often not terribly accurate, though I'd be surprised if they were out by more than say 5%.

Is your container 160 cm³ when filled right to the top, or is the 160 mark slightly below the top?

@JohnRennie It is slightly below the top. It is the same as the cup in this picture pinterest.com/pin/338262621995880382

The sides of that cup are slightly curved so the equation V = ¹⁄₃πh(r₁² + r₁r₂ + r₂²) won't be exactly right.

@JohnRennie I see. So, a square/rectangular or cylinder shaped would be much easier to accurately calculate volume in terms of liters, ml, etc. then.

@JohnRennie like most food containers.

@JohnRennie did that curve explain why the water comes out from that will be slightly have higher volume from the one that comes from measuring cups that have no curve?

@SnoopyKid I suspect it's just that the scale on the container isn't very accurate.

@JohnRennie yeah I think so.

@JohnRennie so I use the formula V = ¹⁄₃πh(r₁² + r₁r₂ + r₂²), 1/3 x 22/7 x (4^2+(4+4)+4^2) x 8 and I got 335.239 so it is approximately 336 ml. Then I tried the usual formula to find volume which is LxWxH = 8x8x8 which is equal to 512 and then divide by 1000 and I got 0.512 which is equal to 512 ml. Why the difference?

Because when you use the formula V = ¹⁄₃πh(r₁² + r₁r₂ + r₂²) with r₁ and r₂ equal you are calculating the volume of a cylinder.

When you calculate 8 x 8 x 8 you are calculating the volume of a cube.

And the volume of a cylinder and cube are different.

@JohnRennie ok so with round food containers, we use the former formula while for square and rectangular food containers we use the latter?

round containers example (containerstore.com/s/kitchen/food-storage/leftovers-glass/Glass/…), squarish and rectangular food containers examples (pinterest.com/pin/517984394644333232)

@SnoopyKid yes

what is the significance of the fermi energy level?

@satan29 It's a very broad question, I think you should study what you are interested in from a good book (or even wikipedia) and maybe ask about specific things

i am studying semiconductor physics

and my book keeps mentioning the position of the fermi level in a matell/insulator/semiconductor/doped semiconductor

i read fermi-diract statistics, and to me it just appears that its like some constant...I dont see why where the fermi level lies in various solids is relevant?

how is possible to increase visibility for questions if you don't have enough reputation to open a bounty?

Like the book was careful enough to mention that the fermi level shifts up slightly, in an n-type semiconductor.but why does that matter? It does not seem to be a valid energy state for an electron....so whats the point

@AstroFedale Sorry, there isn't much you can do. If you have some useful info to enhance the question, like refs to relevant papers, you can edit that into the question. The edit will bump the question to the front page (and the Active tab), which makes it more visible. But please don't make a trivial edit just to bump your question. That tends to annoy people.

BTW, you can post cosmology questions on astronomy.stackexchange.com/questions It's less busy than Physics.SE, so questions stay on the front page longer. And most of the Physics.SE members who know about cosmology & astrophysics tend to visit Astronomy.SE. It's not a good idea to cross-post the same question to two or more sites at the same time, but if you still don't get an adequate answer in a week or two, consider posting a new version on Astronomy.SE.

@PM2Ring Thank you , I didn't know about astronomy stackexchange. if/when I post in astronomy, should I delete the question here to avoid duplicate or I can leave it without problems?

@AstroFedale Well, your question has a positive scored answer, so you can't delete it.

@PM2Ring Ah, didn't know that. Thanks for letting me know

If you do post in Astronomy, you can link to your Physics question, and explain what further info you need that isn't adequately covered by the existing answer(s).

hi