Error Propagation for Tube Volume

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Homework Statement

You have a cylindrical tube for which you know the length is 16±0.1 cm and the radius is 8±0.1 cm, what is the error of the volume?

Homework Equations

The Attempt at a Solution

V = π*8²*16 = 3216.99 cm

But since the r term is squared, must we account for its error twice in the error propagation equation?

σ_V = 3216.99*√((0.1/16)²+(0.1/8)²+(0.1/8)²

Or does this require only one (0.1/8)² term?

 

[haruspex]

The general formula you quote for combining uncertainties assumes the errors are independent. That is clearly not the case when two variables are the same, so you cannot treat rⁿ as n instances of independent variables with the same error distribution as r.
See http://en.wikipedia.org/wiki/Propagation_of_uncertainty#Example_formulas.