For full credit indicate clearly how you reached your answer. Each problem is worth 3 points.
 

1. Find the volume of the solid bounded above by the paraboloid f(x,y) =  and below by the xy-plane.
 
 
 

2. Find the center of mass of the paraboloid in problem 1 if it is composed of material with uniform density.
 
 
 

3. Find the center of mass of a planar region of uniform density shaped like a right triangle with legs of lengths a and b.
 
 
 

4. Pat the mathematician has decided to go into business producing mathematically perfect bookends shaped like the first-octant portion of the solid under the surface f(x,y) = 9 - (x + y)². Find the center of mass of Pat's bookends if they are made of a material with uniform density.
 
 
 

5. Set up an integral for the surface area of the portion of  below the plane z=h.