Answer
$900 \pi$
Work Step by Step
The flux through a surface can be defined only when the surface is orientable.
We know that $\iint_S F \cdot dS=\iint_S F \cdot n dS$
Here, $n$ denotes the unit vector.
Since, $\iint_S f(x,y,z) dS \approx \Sigma_{i=1}^n f(\overline(x), \overline(y), \overline(z)) AS_i$
Here, the four parts have the same surface area and the area of each of the four quarter cylinders is $\dfrac{4 \pi r^2}{8}=\dfrac{ \pi (50)}{2}= 25\pi$
Thus, $\iint_S F(x,y,z) dS =25 \pi[7+8+9+12]=900 \pi$
