Error Propagation for Tube Volume

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SUMMARY

The discussion focuses on calculating the error propagation for the volume of a cylindrical tube with a length of 16±0.1 cm and a radius of 8±0.1 cm. The volume is calculated using the formula V = π*r²*h, resulting in V = 3216.99 cm³. The error propagation equation is debated, specifically whether to include the radius error term twice due to its squared nature. The consensus is that the error for the radius should be considered only once in the equation, as the errors are not independent.

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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


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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?

σV = 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?
 
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