Vernier Calipers

How to calculate the percentage uncertainty?

The Diameter of a cylindrical piece of copper rod was measured at 24.8+/- 0.05 mm with a vernier caliper. Its length was measured at 135+/-0.5 mm with a metre rule. How do I calculate the percentage uncertainty in the volume of the cylinder? I also have to find out the absolute uncertainty in the volume of the cylinder in mm^3. Please help me with explanation.

When any quantities are multiplied ( or divided) the PERCENTAGE error in each quantity must be added.

If quantities are added or subtracted the ABSOLUTE error in each quantity must be added.

In the formula for volume v =Pi R^2 H
we can rewrite it as a multiplication.

V= Pi * R * R * H
Pi has no error. so only the error in R and H is important.
It is a multiplication so we must add the relative error in R 2 times then add the relative error in H once

The relative error in R is 0.05/24.8 = 0.002 ( 0r 0.2%)
The relative error in H is 0.5/135 = 0.0037 ( or 0.37%)

so the total relative error is 0.2 + 0.2 + 0.37 % = +or - 0.77%

To find the absolute error first find the volume of the rod ( assuming no error) then find 0.77% of that
Your final error would be plus or minus this amount.

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