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Resistance of a fructum-shaped bar

  1. May 21, 2006 #1
    I have to calculate the resistance of a bar that is shaped like a fructum and I'm only given the radius of both ends, not its length.

    The formula to calculate the resistance in general is

    [tex]R = \rho * \frac{l}{A}[/tex]

    And the formula for the volume of a fructum is

    [tex]V = \frac{\pi * l}{3} (r^2_2 * r_2r_1 * r^2_1)[/tex]

    My problem is that I have difficulties incorporating the formula for the volume into the formula for the resistance.

    Would it be possible to calculate the volume of the fructum (which would be dependant on l) and treat it like it's a cube with the same volume? That way, I could use [tex]A = \frac{V}{l}[/tex], then divide the volume by l and enter it into the formula for R.

    Other than that, I have no idea what approach to take.
    Last edited: May 21, 2006
  2. jcsd
  3. May 21, 2006 #2


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    Gold Member

    Sorry, looked as best I can.

    No idea what a fructum is.
  4. May 21, 2006 #3
    Sorry, I misspelled it. I meant a frustum. It's like a cone, but with the "sharp" end cut off.
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