GATE ECE 2021 | Question: 37

Question

For a vector field $D=\rho\cos^{2}\:\varphi \:a_{\rho }+z^{2}\sin^{2}\:\varphi \:a_{\varphi }$ in a cylindrical coordinate system $\left ( \rho ,\varphi ,z \right )$ with unit vectors $a_{\rho },a_{\varphi }$ and $a_{z}$, the net flux of $D$ leaving the closed surface of the cylinder $\left ( \rho =3, 0\leq z\leq 2 \right )$ (rounded off to two decimal places) is ________________