Frustum

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

Strychnos
Posts: 41
Joined: Mon Oct 23, 2006 10:00 pm UTC

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

jestingrabbit
Factoids are just Datas that haven't grown up yet
Posts: 5967
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

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.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

Strychnos
Posts: 41
Joined: Mon Oct 23, 2006 10:00 pm UTC

Re: Conic Frustum

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

ThomasS
Posts: 585
Joined: Wed Dec 12, 2007 7:46 pm UTC

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

CodeLabMaster
Posts: 97
Joined: Sun Aug 05, 2007 5:20 am UTC
Location: Just sum the possible locations times thier probabilities to find where you should expect me...

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?

Hix
Posts: 364
Joined: Sun Oct 15, 2006 5:46 pm UTC

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?

gorcee
Posts: 1501
Joined: Sun Jul 13, 2008 3:14 am UTC

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?

eatnukes
Posts: 2
Joined: Tue Sep 23, 2008 7:18 pm UTC

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)^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.

//

jmorgan3
Posts: 710
Joined: Sat Jan 26, 2008 12:22 am UTC

Re: Conic Frustum

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.
This signature is Y2K compliant.
Last updated 6/29/108

skeptical scientist
closed-minded spiritualist
Posts: 6142
Joined: Tue Nov 28, 2006 6:09 am UTC
Location: San Francisco

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

jmorgan3
Posts: 710
Joined: Sat Jan 26, 2008 12:22 am UTC

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.
This signature is Y2K compliant.
Last updated 6/29/108

Excalibur0998
Posts: 14
Joined: Wed Sep 24, 2008 4:48 am UTC

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.

skeptical scientist
closed-minded spiritualist
Posts: 6142
Joined: Tue Nov 28, 2006 6:09 am UTC
Location: San Francisco

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

eatnukes
Posts: 2
Joined: Tue Sep 23, 2008 7:18 pm UTC

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

Who is online

Users browsing this forum: No registered users and 16 guests