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.










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 .




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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