A building is to have a curved roof above a rectangular base. In relation to a rectangular grid, the base is the rectangular region −30 ≤ x ≤ 30, −20 ≤ y ≤ 20, where x and y are measured in meters. The height of the roof above each point (x, y) in the base is given by h(x, y) = 12 − 0.003x² − 0.005y²

a. Find the volume of the building.

b. Find the average height of the roof.