OpenStax University Physics/E&M/Gauss's Law

For quiz at QB/d_cp2.6
$$\Phi=\vec E\cdot\vec A$$ $$\to\int\vec E\cdot d\vec{A}=\int\vec E\cdot \hat n\,dA$$ = electric flux

$$q_{enclosed}=\varepsilon_0\oint \vec E\cdot d\vec A$$

$$d\,\text{Vol}=dxdydz=r^2drdA$$ where $$dA=r^2d\phi d\theta$$

$$A_{\text{sphere}}=r^2\int_0^\pi \sin\theta d\theta\int_0^{2\pi}d\phi=4\pi r^2$$