Let f(x, y, z) be the density of a solid object bounded by a closed surface B, it is known that II f(x, y, z) dV gives the mass of the solid. Solid stainless steel designs are to be fixed on stair case railings in a house. If each design is bounded below by the cone z = Vx2 +y2 and above by the paraboloid z 2 - x2 - y² with constant density f(x, y, z) = 12, find the mass of the design (You should prefer the cylindrical polar coordinates to the spherical polar coordinates, but be cautious with the r-limits).

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