In all cases below marks will only be awarded for exact answers. No marks will be awarded for decimal approximations. Let T be the cylinder x? + y? < 16, 0 <z<1, and let S be thesurface bounding T. Let v be the vector field \mathbf{v}=\left(5 x y^{2} z+y^{2},-3 x^{2} y+z, 3 x^{2} z+6 y\right) Given that \iint_{S} \mathbf{v} \cdot \mathrm{d} \mathbf{S}=A \pi use the divergence theorem to evaluate the integral. State the valueof A. p. Let be the curved part of the surface S (that is, the surface defined by a2 + y2 = 16, 0 < z < 1). By subtracting the contribution of the flat ends from the previousanswer, or otherwise, evaluate the following integral. \iint_{\Sigma} \mathbf{v} \cdot \mathrm{d} \mathbf{S}=B \pi state the value of B.

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