If the length of a cylinder is `L = (4.00 +-0.01)cm` radius `r = (0.250 +- 0.001)cm` and mass `m = (6.25+- 0.01)g` . Calculate the percentage error in determination of density.

Explanation

Density of cylinder, `rho=(("mass")/("volume")V)=(m)/(pir^(2)l) ( :. V=pi r^(2)l)`
`:.` Relative error in `rho=(Delta rho)/(rho)=(Deltam)/(M)+2(Deltar)/(r)+(Deltal)/(l)`
`=(0.01)/(6.25)+2xx(0.001)/(0.250)+(0.01)/(4.00)`
`=0.0016+0.008+0.0025`
`=:.(Delta rho)/(rho)=0.0121`
`:.` The percentage error in `rho=0.0121xx100=1.2%`