(a) Let E be the solid region in the first octant (i.e., where $x \ge 0$, $y \ge 0$, $z \ge 0$) that is inside the cylinder $x^2 + y^2 = 1$ and below the plane $x + z = 1$. Sketch the solid E and calculate $\iiint_E y \,dV$. Hint: This problem was in PS #12.
(b) Find $\iiint_E \sqrt{x^2 + y^2} \,dV$ where E is the solid region above the xy-plane, below the paraboloid $z = 8 - x^2 - y^2$ and outside the cylinder $x^2 + y^2 = 1$. Sketch the solid E.
