Answer
$|q|==1.0 \times 10^{-7} \mathrm{C}$
$k=8.99 \times 10^9 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}^2$.
Work Step by Step
Let $E=\sigma / 2 \varepsilon_0=3 \times 10^6 \mathrm{~N} / \mathrm{C}$. With $\sigma=|q| / A$, this leads to
$$
|q|=\pi R^2 \sigma=2 \pi \varepsilon_0 R^2 E=\frac{R^2 E}{2 k}=\frac{\left(2.5 \times 10^{-2} \mathrm{~m}\right)^2\left(3.0 \times 10^6 \mathrm{~N} / \mathrm{C}\right)}{2\left(8.99 \times 10^9 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}^2\right)}\\=1.0 \times 10^{-7} \mathrm{C},
$$
where $k=1 / 4 \pi \varepsilon_0=8.99 \times 10^9 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}^2$.
