$3.$ Verify the divergence theorem by evaluating and comparing its left$-$hand side and its right$-$hand side for the vector field $\backslash (\backslash$mathbf$\{$D$\}=\backslash$mathbf$\{$r$\}^\{\backslash$wedge$\}\backslash$mathbf$\{$r$\}^\{3\}\backslash )($given in cylindrical coordinates$)$ in the region between two concentric cylindrical surfaces, defined by $\backslash (\backslash$mathrm$\{$r$\}=0\mathrm{.}5\backslash )$ and $\backslash (\backslash$mathrm$\{$r$\}=1\backslash ),$ with both cylinders extending between $\backslash (\backslash$mathrm$\{$z$\}=0\backslash )$ and $\backslash (\backslash$mathrm$\{$z$\}=2\backslash ).$