Consider the elipsoid 2x2 + y2 + 2z2 = 1 and the sphere x2 + y2 + z2 2z = 0. a. Determine the volume of the region K bounded by this elipsoid and this sphere. b. Determine the equation of the sphere A that is inside the region K, such that it is the biggest sphere possible. c. Determine the volume of this same sphere A using double or triple integrals. Consider the elipsoid 2x2 + y2 + 2z2 = 1 and the sphere x2 + y2 + z2 2z = 0. a. Determine the volume of the region K bounded by this elipsoid and this sphere. b. Determine the equation of the sphere A that is inside the region K, such that it is the biggest sphere possible. c. Determine the volume of this same sphere A using double or triple integrals