14.6   Triple Integrals in Cylindrical and Spherical Coordinates

                                                                  by SGLee - HSKim - VLang- SWSun

1. Find .

                                              .

2. Find the volume of the solid cut from the cylinder   by the sphere of  radius  and centered at the origin.

          as 

         ,   

      .

3. Find the volume cut from the cone  by the sphere .

        .

4. Find the volume of the solid bounded by the spherical surface   

    and the circular cone .

       .

5. Find the volume of the solid  that lies above the cone  and below the sphere

   .

          .

 6. Evaluate  where  and  is the surface whose side  is the cylinder ,

           whose bottom  is the disk  in the plane ,

           and whose top  is the part of the plane  that lies above .

           http://matrix.skku.ac.kr/cal-lab/cal-14-6-2.html  

7. Find the volume of the region common to the intersecting cylinders  and .

8. Find the volume of the region bounded below by the paraboloid  and above by the plane .

9. Find the volume cut from the sphere  by the cylinder .

10. Evaluate , where  is the region inside  in the first octant.

11. Find the volume bounded above by the sphere  and below by the paraboloid .

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