You wish to construct an observatory, which is shaped like a cylinder with a hemispherical dome on top. The material for the walls of the cylinder costs $100 per square foot, while the material for the domed roof costs $200 per square foot. The total volume of the observatory needs to be 2000 cubic feet. What dimensions minimize the cost? (Hint: the volume of a sphere of radius r is 4r2.) Remember to include units!