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 .