Calculate the percentage uncertainty?

The diameter of a cylindrical rod is 24.8 卤 0.05mm. Its length is measured at 135 卤 0.5mm.



Calculate the percentage uncertainty in the volume of the cylinder?



Also Calculate the absolute uncertainty in the volume of the cylinder in mm^3?



Please show working out, I just need to know how to work it out.. not the answer - the answer is not important!



Thanks!Calculate the percentage uncertainty?
What you have here is a number of measurements which will be multiplied together (eg. Volume = X x Y x Z ) (of course, in this case, X and Y are both the same - ie. the diameter, because it will be squared in finding the volume).



In these cases, the rule is: The percentage uncertainty in the answer is the SUM of the percentage uncertainties of each of the products.



Or, put another way,



dV/V = dX/X + dY/Y + dZ/Z (where I have used the shorthand dX to mean 'delta X' or uncertainty in X). Note that fractional uncertainties like dX/X are equivalent to percentage uncertainties - I assume that you know how to switch trivially from one to the other.



So... for you... dV/V = 2 x dD/D + dL/L, where D = diameter and L = Length.



Once you have this, dV = dV/V x V (ie. the absolute uncertainty is the fractional uncertainty x the Volume)



I think this should be enough for you to finish the problem.