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Homework Help: Hieght of a volume in a cylinder on its side, with known volume.

  1. Dec 31, 2007 #1
    This is my first post and is for an applied project (not for a class) but I thought this was the best place to ask for help.


    1. The problem statement, all variables and given/known data
    Given a cylindar on its side, with volume V, length L, and Radius R, what is height (h) of liquid. I have fomula for volume as a function of radius, length, and height, but when I try to solve for h, things get difficult.


    2. Relevant equations
    CylindricalSegment_1002.gif
    and
    http://mathworld.wolfram.com/images/equations/CylindricalSegment/equation2.gif [Broken]

    3. The attempt at a solution
    1) divide both sides by L
    2) square both sides
    3) expand polynomials
    4) get stuck, post this message
     
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Dec 31, 2007 #2
    Did you come up with that formula or was it provided and you have to solve for h?

    [tex]\cos^{-1}(\frac{R-h}{R})=\frac{\mbox{adjacent}}{\mbox{hypotenuse}}[/tex]
     
    Last edited: Dec 31, 2007
  4. Dec 31, 2007 #3
    It was provided for me and I'm trying to solve for h. It is possible that there is a different approach to the problem that solves for h directly (via caluclus) but I have not found it.
     
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