# Math Help - Length per unit volume of a cylinder

1. ## Length per unit volume of a cylinder

Hello (I hope this is the right forum topic for this question)

I am having some difficulty trying to calculate the length per unit volume for a cylinder.

I know the radius of the cylinder. I also know the volume fraction of the cylinder.

I need to calculate the length per unit (total) volume of the cylinders, which is a way to describe the density of cylinders.

Any help with this would be greatly appreciated. Thanks.

2. ## Re: Length per unit volume of a cylinder

Hey jespl1.

Which length are you referring to? Are you talking about the height of the cylinder with respect to the volume given that particular height?

3. ## Re: Length per unit volume of a cylinder

A cylinder of radius r has volume $\pi r^2 h$. The "volume per unit length" is, taking h=1, $\pi r^2$ so "length per unit volume" must be $\frac{1}{\pi r^2}$.

4. ## Re: Length per unit volume of a cylinder

The length per unit volume refers to the length of the cylinders with respect to the entire sample volume. Think of a collection of cylindrical objects floating in some water. All the cylinders have the same radius and there is a certain fraction of the overall volume occupied by the cylinders. I think I have figured this out though. The length per unit volume = the volume fraction/(pie x radius^2) (sorry I don't know how to use mathematical symbols etc>)

5. ## Re: Length per unit volume of a cylinder

You said "length per unit volume so your "volume fraction" is 1. That gives the answer I gave above.