A silo is to be constructed in the form of a cylinder surmounted by a hemisphere. The cost of construction per square foot surface area is twice as much for the hemisphere as for the cylinder. Determine the dimensions to be used if the volume is fixed (100m^3) and the cost is to be minimum.
Surface area times cost = 2x PI r h + 2x pi r^2 + 4x pi r^2 x being the cost Volume = pi r^2 h +(2/3) pi r^3 =100 pi r^2 h =100 - (2/3) pi r^3 h = 100 / pi r^2 - (2/3) r ---(1) cost=2x PI r h + 2x pi r^2 + 4x pi r^2 plug in 'h' from (1) and differentiate w.r.t 'r' set this equal to 0 and solve for r
