Each problem is worth 5 points.

1. Set up a triple integral and use it to find the volume of the solid bounded by z=x²+y² and z=2x+2y.
 
 

2. Set up triple integrals and use them to find the centroid of the solid bounded by z=x²+y² and z=2x+2y.
 
 

3. [Stewart 4^th §16.6 #22] Find the surface area of the solid that lies within both the cylinders x²+z²=r² and y²+z²=r².
 
 

4. Set up triple integrals and use them to find the centroid of the solid in the first octant bounded by x+y=1, x+z=1, and y+z=1.
 
 

5. Set up triple integrals and use them find the centroid of the solid between the plane z=0 and the surface z=a-x²-y² in terms of a.
 
 

6. Find the surface area of the solid between the plane z=0 and the surface z=a-x²-y² in terms of a.