Propagation of Uncertainty - Hollow Cylinder

[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. Homework Statement

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

Homework Equations

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

The Attempt at a Solution

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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 extremely grateful. Thank you.

 

[gneill]

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)?