1. (Polar) Find the volume of a right circular cone with base radius a and height h using polar coordinates.

2. (Polar) Find the volume of the solid bound by the paraboloids z = 2x2 + 2y2 and z = 3 x2 y2.3. (Surface Area) Find the surface area of the paraboloid z = 5x2y2 which lies in the first octant (x, y, z 0).4. (Triple Int: Setting up bounds) Find the mass of the region bounded by the planes x+y+z = 1, x+y+z = 1,

the xz plane, and the xy plane with density (x, y, z) = y2.

5. (Triple Int: Setting up bounds) Evaluate the triple integral

E y dV where E is the solid that lies underthe plane z = 3x+ 3y and above the triangular region in the xy-plane with vertices (0, 0), (1, 0), and (1, 1).

6. (Triple Int: Switching orders) Consider the integral 10

10

1zz1 f(x, y, z) dx dy dz. Switch the order of inte-

gration to dy dz dx.

7. (Triple Int: Switching orders) Evaluate the integral 10

1x

1y0 x dz dy dx, and then rewrite the integral in

another order (you do not need to re-evaluate the new integral).

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