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when i solved by $ \iint F\cdot ndS $ ,i get an answer $a^2 h$ but on solving by $ \iiint \nabla\cdot F dxdydz $ ,i get $π a^2 h^2$. I would want to attach my work but I am not familiar with LaTeX and it would take me ages.

I would greatly appreciate if anyone guides me through the answer.

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    check correctly it's exactly $\pi a^2 h^2$ for both the case. – 2017-01-09

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Your volume integral is ok.For surface integral consider the surface (i)$S_1(z=0)$ (ii)$S_2(z=h)$(iii)$S_3$ on curved surface.

$\iint s_1\,ds_1=\iint s_3\,ds_3=0$

For $S_2(z=h)$:$F(x,y,z)=y\hat{i}+x\hat{j}+h^2\hat{k}$ and $\hat n=\hat k$

$\iint F.\hat n\, ds_2=h^2\iint ds_2=h^2\pi a^2$

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    Is integral over s3=0 becoz we end up having integration of sin2t where t goes from 0 to 2pi? – 2017-01-10
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    And how about i use the formula $ \iint F.n ds$ = $ \iint F.n dx dz /|n.j| $ ? – 2017-01-10