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Given the solid S: z=x^2 + 4y^2 , z <= 16 Find the volume and surface area of the solid S
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$$A = \int_S \,dS = \iint_T \left\|{\partial \mathbf{r} \over \partial x}\times {\partial \mathbf{r} \over \partial y}\right\| dx\, dy = \iint_T \sqrt{\left({\partial f \over \partial x}\right)^2+\left({\partial f \over \partial y}\right)^2+1}\, \, dx\, dy $$