Use cylindrical coordinates to find the volume of the solid between two sheets of the hyperboloid z^{2} =64+x^{2}+y^{2} bounded by the cylinder x^{2}+y^{2}=225. (HINT: Use symmetry and elementary geometry to simplify the calculation.)
Use cylindrical coordinates to find the volume of the solid between two sheets of the hyperboloid z^{2} =64+x^{2}+y^{2} bounded by the cylinder x^{2}+y^{2}=225. (HINT: Use symmetry and elementary geometry to simplify the calculation.)
so , in cylindrical coordinates, is the cylinder with axis the z-axis and radius 15. The hyperboloid is or in cylindrical coordinates. The volume of the region between the two branches of the hyperbola, inside the cylinder, is given by .