Frustum
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Frustum
Someone showed me this problem and I'm completely stumped as to how to do it.
You're supposed to calculate the volume of the frustum, only given the inputs of Hbig, Hsmall, and Rbig. I assume you have to find the volume of the entire cone and subtract off the smaller bit, but I have no idea how to get the volume of the smaller bit itself.
Any tips?
You're supposed to calculate the volume of the frustum, only given the inputs of Hbig, Hsmall, and Rbig. I assume you have to find the volume of the entire cone and subtract off the smaller bit, but I have no idea how to get the volume of the smaller bit itself.
Any tips?
Last edited by Strychnos on Wed Sep 24, 2008 2:56 am UTC, edited 1 time in total.
 jestingrabbit
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Re: Conic Frustum
Strychnos wrote:I have no idea how to get the volume of the smaller bit itself.
Any tips?
The smaller bit is a cone.
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Re: Conic Frustum
Right, but how would I find the radius of that cone? We are only given values of Hbig, Hsmall, and Rbig.
Re: Conic Frustum
Strychnos wrote:Right, but how would I find the radius of that cone? We are only given values of Hbig, Hsmall, and Rbig.
There is an underlying 2d geometry problem regarding the relationship between Hbig, Rbig, Hsmall, and Rsmall. Something involving triangles and similarity.
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Re: Conic Frustum
Take a cross section of the frustum. What does it look like to you? Regardless of what it looks like, how would you solve for what you need?
Re: Conic Frustum
Suppose one cone was three times taller than the other one. How would you expect their radii to compare? Can you prove it?
Re: Conic Frustum
Slice the cone in half from top to bottom.
Dip the edges in paint.
Place the edges on a sheet of paper. What shape do you have?
Dip the edges in paint.
Place the edges on a sheet of paper. What shape do you have?
Re: Conic Frustum
You can also set the volume of the frustum equal to the volume of the large cone minus the small cone and solve for the small radius
You get :
Rsmall = (Rlarge((12(hf)^24hf*hsmall+4hf*hlarge+hlarge*hsmall)^(1/2)2hf))/(4hf+hsmall)
where hf = hlargehsmall
I believe my math is correct, I'm too lazy to test it.
ps. You probably shouldn't post your engineering homework on a forum that shows up as the second entry when you Google "conic frustum"
Now that it's already past the due date, I don't feel too bad about posting this, however.
//
You get :
Rsmall = (Rlarge((12(hf)^24hf*hsmall+4hf*hlarge+hlarge*hsmall)^(1/2)2hf))/(4hf+hsmall)
where hf = hlargehsmall
I believe my math is correct, I'm too lazy to test it.
ps. You probably shouldn't post your engineering homework on a forum that shows up as the second entry when you Google "conic frustum"
Now that it's already past the due date, I don't feel too bad about posting this, however.
//
Re: Conic Frustum
Just find the area of the volume of rotation of f(x)=x * (R_{big} / H_{big}) about the xaxis from H_{small} to H_{big}. The equation you come up with should be this:
EDIT: New info. See below.
Spoiler:
EDIT: New info. See below.
Last edited by jmorgan3 on Wed Sep 24, 2008 2:13 am UTC, edited 1 time in total.
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 skeptical scientist
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Re: Conic Frustum
*smacks jmorgan upside the head*
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.
"With math, all things are possible." —Rebecca Watson
"With math, all things are possible." —Rebecca Watson
Re: Conic Frustum
skeptical scientist wrote:*smacks jmorgan upside the head*
*Politely asks SS not to do that again.*
If your problem is that I made an error (it's been a while since AP Calc), then tell me and I'll change it. If your problem is that I gave him an answer, then I respond that anyone who can't solve a simple geometry problem with the hints provided probably doesn't even know the meaning of the [imath]\int[/imath] symbol.
EDIT: Something called a "search box" informs me that he is in calculus. Equation has been redacted.
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Re: Conic Frustum
eatnukes wrote:ps. You probably shouldn't post your engineering homework on a forum that shows up as the second entry when you Google "conic frustum"
Now that it's already past the due date, I don't feel too bad about posting this, however.
//
Haha, I was thinking the same thing. I wonder if the OP goes to Virginia Tech, because this problem was due yesterday. This exact same problem.
Similar triangles have the same ratio of side lengths. You can make a ratio like Hbig : Hsmall as Rbig : Rsmall.
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Re: Conic Frustum
jmorgan3 wrote:skeptical scientist wrote:*smacks jmorgan upside the head*
*Politely asks SS not to do that again.*
If your problem is that I made an error (it's been a while since AP Calc), then tell me and I'll change it. If your problem is that I gave him an answer, then I respond that anyone who can't solve a simple geometry problem with the hints provided probably doesn't even know the meaning of the [imath]\int[/imath] symbol.
EDIT: Something called a "search box" informs me that he is in calculus. Equation has been redacted.
It was in good fun. What I meant is that using an integral/solid of rotation methods to find the volume of a cone minus a smaller cone seems like huge overkill, and probably not the least bit helpful to the OP. What I meant was that I found your post funny, but of the type of joke that makes you want to smack the teller upside the head while trying not to find it funny.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.
"With math, all things are possible." —Rebecca Watson
"With math, all things are possible." —Rebecca Watson
Re: Conic Frustum
skeptical scientist wrote:jmorgan3 wrote:skeptical scientist wrote:*smacks jmorgan upside the head*
*Politely asks SS not to do that again.*
If your problem is that I made an error (it's been a while since AP Calc), then tell me and I'll change it. If your problem is that I gave him an answer, then I respond that anyone who can't solve a simple geometry problem with the hints provided probably doesn't even know the meaning of the [imath]\int[/imath] symbol.
EDIT: Something called a "search box" informs me that he is in calculus. Equation has been redacted.
It was in good fun. What I meant is that using an integral/solid of rotation methods to find the volume of a cone minus a smaller cone seems like huge overkill, and probably not the least bit helpful to the OP. What I meant was that I found your post funny, but of the type of joke that makes you want to smack the teller upside the head while trying not to find it funny.
Like trying to explain relativity to middle schoolers using the math, rather than the 3 trees and lightning picture...
@Excalibur: yes, yes it was. =D
I would assume for my own safety, however, that he is a friend of an engineering student, not one himself. Personally I see no problem asking for help though, the real assignment was about the flowchart rather than the math insofar as i could tell.
//
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