# Thread: How to find cylinder dimensions from volume and aspect ratio?

1. ## How to find cylinder dimensions from volume and aspect ratio?

Okay, so basically what I'm trying to figure out is how to find the dimensions (length and diameter) of a cylinder when I know the volume and the ratio of length to diameter (for instance, a cylinder x times longer than it is wide). Unfortunately, I haven't been able to figure out how to do so on my own and google hasn't exactly been helpful. I'm quite stumped, so I would greatly appreciate any help.

2. I expect when you say length you mean height...

You should know that $\displaystyle \displaystyle V = \pi r^2 h$.

If you know the ratio of height to diameter/radius, you'll be able to substitute it into the volume equation and solve for one of the variables.

3. ## Re: How to find cylinder dimensions from volume and aspect ratio?

I have a similar problem. Diameter=height, Volume = 50m^3
so... r=D2 and h=D
V=pi*h*r^2
V=pi*D*(D/2)^2
V/pi=D*(D/2)^2

PEMDAS is confusing me, can I...

V/pi=D*(D/2)*(D/2)
V/pi=D^3 / 4
?

4. ## Re: How to find cylinder dimensions from volume and aspect ratio?

Originally Posted by mstngofire
I have a similar problem. Diameter=height, Volume = 50m^3
so... r=D2 and h=D
V=pi*h*r^2
V=pi*D*(D/2)^2
V/pi=D*(D/2)^2

PEMDAS is confusing me, can I...

V/pi=D*(D/2)*(D/2)
V/pi=D^3 / 4
?
$d^3 = \dfrac{4V}{\pi}$

$d = \sqrt[3]{\dfrac{4V}{\pi}}$

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# calculating the ratio of the cylinder height

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