24. (Accuracy) Let $S$ be the funnel-shaped surface defined by $x^2 + y^2 = z^2$ for $1 \le z \le 3$ and $x^2 + y^2 = 1$ for $0 \le z \le 1$.
(a) Sketch a cross section of the surface in the $xz$ plane.
(b) Evaluate
$\iint_S \langle -y, x, z \rangle \cdot \mathbf{n} \, dS$
if $S$ has normals oriented away from the inside of the funnel.
Hint: Split the surface integral into two surfaces $S_1$ and $S_2$ where $S_1$ is the surface for $0 \le z \le 1$ and $S_2$ the remaining surface. Then use the fact that
$\iint_S \langle -y, x, z \rangle \cdot \mathbf{n} \, dS = \iint_{S_1} \langle -y, x, z \rangle \cdot \mathbf{n} \, dS + \iint_{S_2} \langle -y, x, z \rangle \cdot \mathbf{n} \, dS.$
