Answer
$900 \pi$
Work Step by Step
When the surface is orientable then the flux through a surface is defined as: $\iint_S F \cdot dS=\iint_S F \cdot n dS$
where, $n$ is the unit vector.
Since, we have $\iint_S f(x,y,z) dS \approx \Sigma_{i=1}^n f[\overline{x}, \overline{y}, \overline{z}] AS_i$
Four parts with the same surface area and the area of each of the four quarter part of the cylinder is given by:
$\dfrac{4 \pi r^2}{8}=\dfrac{ \pi (50)}{2}= 25\pi$
Hence, we have $\iint_S F(x,y,z) dS =25 \pi[7+8+9+12]=900 \pi$
