A grain silo consists of a cylindrical concrete tower surmounted by a metal hemispherical dome. The metal in the
dome costs 1.5 times as much as the concrete (per unit of surface area). If the volume of the silo is 750 m cubed, what are the dimensions of the silo(radius and height of the cylindrical tower) that minimize the costs of the materials? Assume the silo has no floor and no flat ceiling under the dome.