# Propagation of Uncertainty - Hollow Cylinder

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1. Sep 14, 2016

### Godisnemus

Hi, I'm having quite a bit of trouble finding the propagation of uncertainty (using partial derivatives) of the volume of a hollow cylinder. The examples in my tutorial only demonstrates how to find the propagation of uncertainty on simple operations such as x + y, x/y, etc...

1. The problem statement, all variables and given/known data

Height: h = 10.05 mm ; Δ h = +- 0.05 mm

Outer Diameter: D = 6.03 mm ; Δ d = +- 0.05 mm

Inner Diameter: d = 3.01 mm ; Δ d = +- 0.05 mm

2. Relevant equations

Volume: V = (Pi/4) ((D^2) - (d^2)) (h) = 215.49mm

3. The attempt at a solution

As I've stated above, I have no idea how to find the propagation of uncertainty for such a function using partial derivatives. I've looked a fair amount of time on the web but nearly every example given does not contain more then a single or double variable function. If somebody could give me a step-by-step on how to do this, I would be extremly grateful. Thank you.

2. Sep 14, 2016

### Staff: Mentor

Helpers can't give you a step by step solution here at PF. That's against the forum rules. They can give you hints and suggestions and point out mistakes, but you need to do most of the work and show your efforts.

Suppose this problem had only two variables, say the volume was a function of two variables x and y: V = f(x,y). How would you proceed (in general terms)?

Last edited: Sep 14, 2016