Frustum

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Strychnos
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Frustum

Postby Strychnos » Tue Sep 23, 2008 4:00 pm UTC

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?
Last edited by Strychnos on Wed Sep 24, 2008 2:56 am UTC, edited 1 time in total.
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jestingrabbit
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Re: Conic Frustum

Postby jestingrabbit » Tue Sep 23, 2008 4:03 pm UTC

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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Strychnos
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Re: Conic Frustum

Postby Strychnos » Tue Sep 23, 2008 4:10 pm UTC

Right, but how would I find the radius of that cone? We are only given values of Hbig, Hsmall, and Rbig.
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ThomasS
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Re: Conic Frustum

Postby ThomasS » Tue Sep 23, 2008 4:19 pm UTC

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 2-d geometry problem regarding the relationship between Hbig, Rbig, Hsmall, and Rsmall. Something involving triangles and similarity.

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CodeLabMaster
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Re: Conic Frustum

Postby CodeLabMaster » Tue Sep 23, 2008 4:36 pm UTC

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?

Hix
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Re: Conic Frustum

Postby Hix » Tue Sep 23, 2008 4:54 pm UTC

Suppose one cone was three times taller than the other one. How would you expect their radii to compare? Can you prove it?

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Re: Conic Frustum

Postby gorcee » Tue Sep 23, 2008 8:04 pm UTC

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?

eatnukes
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Re: Conic Frustum

Postby eatnukes » Tue Sep 23, 2008 10:24 pm UTC

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)^2-4hf*hsmall+4hf*hlarge+hlarge*hsmall)^(1/2)-2hf))/(4hf+hsmall)
where hf = hlarge-hsmall

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.

//

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jmorgan3
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Re: Conic Frustum

Postby jmorgan3 » Wed Sep 24, 2008 1:07 am UTC

Just find the area of the volume of rotation of f(x)=x * (Rbig / Hbig) about the x-axis from Hsmall to Hbig. The equation you come up with should be this:
Spoiler:
Nothing to see here. Move along.


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

Postby skeptical scientist » Wed Sep 24, 2008 1:10 am UTC

*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.

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jmorgan3
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Re: Conic Frustum

Postby jmorgan3 » Wed Sep 24, 2008 1:20 am UTC

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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Excalibur0998
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Re: Conic Frustum

Postby Excalibur0998 » Wed Sep 24, 2008 4:56 am UTC

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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skeptical scientist
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Re: Conic Frustum

Postby skeptical scientist » Wed Sep 24, 2008 5:03 am UTC

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

eatnukes
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Re: Conic Frustum

Postby eatnukes » Thu Sep 25, 2008 3:51 am UTC

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 flow-chart rather than the math insofar as i could tell.
//


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