What Is the % Error in the Density of a Metal Bar?

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To determine the percentage error in the density of a metal bar, the relevant formulas for volume (V = πr²h) and density (D = m/V) must be applied. Given the precision of measurements—length at ±1%, mass at ±2%, and radius at ±3%—the propagation of these errors needs to be calculated. The total percentage error in density can be derived from the individual percentage errors of mass and volume, considering that volume is affected by the radius squared and the height. For accurate calculations, resources or textbooks on error propagation in physics are recommended for further understanding. Calculating the density's percentage error is essential for precise measurements in scientific contexts.
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Homework Statement



A metal bar has a length measured to a precision of +-1%, a mass measured to +-2% and a radius masured to +-3%. What would be the % error in the value of the density of the metal in the bar calculated from these?

Homework Equations



V=(pi)r^2h
D=m/v

The Attempt at a Solution



I can calculate the actual density no problem.

However, i was away while we studies calculating with errors and am stuck.

If someone could help me with this problem or recommend a site/book i use to catch up, i'd really appreciate it :).
 
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I have replied to this on TSR
 
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