The density ρ \rho\,ρ of a uniform metal cylinder can be determined using the equation
ρ=Mπr2L \rho = \frac{M}{\pi r^2 L} ρ=πr2LMwhere M M\,M is the mass of the cylinder, r r\,r is its radius, and L L\,L is its length.
The percentage uncertainty in r r\,r is 1.6% and the percentage uncertainty in L L\,L is 2.5%. The percentage uncertainty in M M\,M is negligible.
What is the percentage uncertainty in ρ\rhoρ?
4.1%4.1\%4.1%
5.7%5.7\%5.7%
6.6%6.6\%6.6%
8.2%8.2\%8.2%