Answer
$q = 1.4\times 10^{-7}~C$
Work Step by Step
We can draw a Gaussian cylinder of radius $r = 4.0~cm$ and length $L = 28~cm$ that has the same axis as the charged cylinder.
We can find the required charge $q$:
$\epsilon_0~\Phi = q$
$q = \epsilon_0~E~2\pi~r~L$
$q = (8.854\times 10^{-12}~F/m)~(2.3\times 10^5~N/C)~(2\pi)~(0.040~m)~(0.28~m)$
$q = 1.4\times 10^{-7}~C$
