Answer
$900 \pi$
Work Step by Step
Since, $\iint_S F \cdot dS=\iint_S F \cdot n dS$
where, $n$ denotes the unit vector.
and $dS=n dA=\pm \dfrac{(r_u \times r_v)}{|r_u \times r_v|}|r_u \times r_v| dA=\pm (r_u \times r_v) dA$
The flux through a surface can be defined only when the surface is orient-able.
Since, $\iint_S f(x,y,z) dS \approx \Sigma_{i=1}^n f(\overline(x), \overline(y), \overline(z)) AS_i$
The four parts of the surface consists of the same surface area and the area of each part is given by: $\dfrac{4 \pi r^2}{8}=\dfrac{50 \pi}{2}= 25\pi$
Thus, we have $\iint_S F(x,y,z) dS =25 \pi[7+8+9+12]=900 \pi$
