I am given a vector field $\vec{F}=z\hat{i}+x\hat{j}+y\hat{k}$.

The flux of the vector field passing through the curved surface of the cylinder $x^2+y^2=a^2$ in the first octant and below $Z=h$ plane is calculated to be :- $\frac{1}{2}ah(a+h)$ by me, but the answer discussed by the fellow mates is coming somewhat to be $h^2$.

I need your opinion on this.
If I am wrong, what possible mistake I would be making.