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Mean radius of a cylinder

  1. Nov 6, 2008 #1
    1. The problem statement, all variables and given/known data

    I am working a homework problem that is trying to find the mean radius, [tex]\bar{r}[/tex] from the midpoint of a cylinder.

    The problem states:
    What is the mean radius, [tex]\bar{r}[/tex] from the midpoint of a cylinder of radius a and height h to its boundary surface? Evalute mean radius [tex]\bar{r}[/tex] for a = h/2 = 10 cm.

    2. Relevant equations

    The relavent equation is [tex]\bar{r}[/tex] = (1/4pi)[tex]\int[/tex][tex]\int^[/tex] r sin[tex]\vartheta[/tex]d[tex]\vartheta[/tex]d[tex]\beta[/tex]

    3. The attempt at a solution
    The problem and formula above is from Attix's textbook. In this case I think the limits for beta need to be 0 to 2pi for a cylinder.

    I'm not sure what the limits for theta should be. I'm think it's 0 to pi.
    I need to express r in terms of theta - but I'm not sure how.

    Attix gives the answer as 11.32 cm.

    Thanks in advance for any assistance.
  2. jcsd
  3. Nov 6, 2008 #2


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    Homework Helper
    Gold Member

    I would use cylindrical coordinates [itex](s,\phi,z)[/itex] if I were you...the distance from the center of the cylinder (the origin) to a general point on the cylinder [itex](s,\phi,z)[/itex] is then [itex]\sqrt{s^2+z^}[/itex]...then all you need to do is average that over all three surfaces of the cylinder.

    What is the general formula for averaging a function over a surface [itex]\mathcal{S}[/itex]?...Use that.
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