Discussion
The volume under the surface \( z = f(x,y) \) above a region \( R \) is
Answer: C
Each element of the base carries a column of height \( f \) and base area \( dA \), so its volume is \( f\,dA \) and
\[ V \;=\; \iint_{R} f(x,y)\,dA. \]
The squared integrand with \( \pi \) belongs to a solid of revolution, whose slices are discs rather than columns, and the square root form gives a surface area
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