A silo (base not included) is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square unit of surface area is 7 times as great for the hemisphere as it is for the cylindrical sidewall. Determine the dimensions to be used if the volume is fixed at 14000 cubic units and the cost of construction is to be kept to a minimum. Neglect the thickness of the silo and waste in construction. What is the radius of the cylindrical base? Thanks.
