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Geometry problem: a cone meeting a cylindre.

  1. Oct 8, 2010 #1
    Hi,

    I have a cone on the z axis with his summit on height h meeting a cylinder on the x axis. The expressions should be:

    cylinder: y2+z2=r2

    cone: x2+y2 =(z-h)2tan(phi)2

    If we consider any straight line on the cone, what is the lenght of this line inside the cylinder?

    Is it possible to get a theorical exprssion of this?

    I tried the approche of the distance between two points, but i need a third equation to know the three coordinates of each points. Any ideas?

    Thanks a lot,

    Alx
     
  2. jcsd
  3. Oct 8, 2010 #2

    tiny-tim

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    Welcome to PF!

    Hi Alx! Welcome to PF! :smile:

    (have a phi: φ :wink:)
    the third equation will be a linear one, for a particular line :smile:
     
  4. Oct 8, 2010 #3
    Thanks for your response.

    In fact, I need an expression of the length for ANY line if possible at all.

    My problem goes much deeper: I need to find the mean length for all lines for all Φ...

    All I have to do is to find an expression only in function of Φ and integrate it on all Φ. As simple as it sounds, I can't figure it out, cuz it's far from simple. I've done it in 2D (a triangle passing through a circle) and it worked, so i know my approach is good.

    Anyway, I'll take any hint I get.

    Tanks again,

    Alx
     
  5. Oct 8, 2010 #4

    tiny-tim

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    Hi Alx! :smile:

    I know it's complicated, but you'll just have to work through it. :redface:

    Use y = xtanθ, find the length, and average over θ :wink:
     
  6. Oct 8, 2010 #5

    I think you mean ...

    [tex]x^2 + y^2 = \frac{(h-z)^2}{tan^2\phi}[/tex]
     
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