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Math Help - h of cylinder, given volume and h->r ratio

  1. #1
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    Nov 2009
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    Question h of cylinder, given volume and h->r ratio

    Ok, so I'm trying to post on some forums, and I came up against a hell of a problem. I tried it many ways round, and here is my most perfect, most recent attempt:

    Code:
    Look at a preview of a Raven.  It'll say its length in the top-left corner.
    
    Now look at the attributes of a cruise missile.  0.1m^3 or something volume.  How long can the thing be at that volume?  According to http://science.howstuffworks.com/cruise-missile2.htm  6.25h=0.26r  (6.25m long, h in standard notation, .52m wide, d in standard notation, d=2r, r=d/2, r=.52/2=.26) is implied.
    
    Assuming a perfectly cylindrical cruise missile, we can work some **** out.
    
    6.25h=0.26r
    thus h=(0.26r)/6.25
    thus h=0.0416r
    
    V is volume.
    
    V=(pi)(r^2)h
    
    V=0.1
    
    thus 0.1=(pi)(r^2)0.0416r  (Substitute out h in terms of r.)
    thus 0.1=(pi)0.0416r^3
    thus 0.1/0.0416=(pi)r^3
    thus (0.1/0.0416)/(pi)=r^3
    thus ((0.1/0.0416)/(pi))^(1/3)=r = 0.9146443701959527  (According to Python.  Good enough for EVE, good enough for me.)
    
    h=0.0416r
    thus h=0.0416*[that mess three lines up]
    thus h=0.03804920580015163
    As you can see, h<<r. That really shouldn't be happening, seeing as the thing's gonna be longer than it is wide.

    If anyone could point me in the right direction, I have several cookies on offer, because damn, cookies win.
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  2. #2
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    Joined
    Feb 2010
    Posts
    66

    Finding "h"

    You'll have to check your numbers yourself, but I'd go for the general solution first, then plug and chug:

    Suppose you are given the volume, V and the ratio r/h = G

    Then V = Pi*r^2h and r = Gh

    So V = Pi*(Gh)^2*h = PiG^2*h^3

    Then h = [cube root of] {V/(Pi*G^2)}

    Numbers don't lie. Ask any government tax worker.
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