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

1. ## 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.

2. ## 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.