Laboratory on Spherical Volumes

Problem #1

1. Draw the region in the xy plane, the floor and the ceiling associated with the integral .
   
   
2. Translate the volume into spherical coordinates.
   
   
3. Express the integral in the form .
   
   

Problem #2

Place a small piece of a sphere with in your 3D Kit. Using the variables r, , and define the length, width, and height of the piece if we approximate it as a cube. HINT: solution is .