$($a$)$ The current density in a cylindrical wire of radius $R=2\mathrm{.}0mm$ is uniform across a cross section of the wire and is $J=2\mathrm{.}0{10}^5\frac{A}{m^2}.$ What is the current through the outer portion of the wire between radial distances $\frac{R}{2}$ and $R$

$($b$)$ Suppose, instead, that the current density through a cross section varies with radial distance $r$ as $J=a{r}^2,$ in which $a=3\mathrm{.}0{10}^{11}\frac{A}{m^4}$ and $r$ is in meters. What now is the current through the same outer portion of the wire?

Remember current density and current are related by

$I={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$vec$(J)*dvec(A)$