A cylindrical wire of mass ( 0 . 4 ± 0 . 01 ) g has length ( 8 ± 0...

The formula to calculate the density of the material of the wire is given by

$ρ = \dfrac{M}{{\pi R}^{2}L} . . . \left(1\right)$

Hence, the formula to calculate the percentage error in calculating the density of the material can be written as

$\dfrac{dρ}{ρ} \times 100 = \left[\dfrac{dM}{M} + \dfrac{2dR}{R} + \dfrac{dL}{L}\right] \times 100 . . . \left(2\right)$

Substitute the values of the known parameters into equation (2) to calculate the required percentage error.

\begin{cases} & = & \left[\dfrac{0 . 01}{0 . 4} + \dfrac{2 \times 0 . 03}{6} + \dfrac{0 . 04}{8}\right] \times 100 \\ & = & 4 %\end{cases}