A grain silo has the shape of a right circular cylinder surmounted by a hemisphere (see the figure below). If the silo is to have a capacity of 478π ft3, find the radius and height of the silo that requires the least amount of material to construct. Hint: The volume of the silo is V, and the surface area (including the floor) is S, as shown in the equations below. (Round your answers to two decimal places.)V = πr2h + (2/3)πr3S = π(3r2 + 2rh)it wants to know a value for r and a value for h..I'd appreciate any help I can get!!! thanks!!
V = πr2h + (2/3)πr3=478π ---> h = (478/r^2) -(2/3)r and S = π(3r2 + 2rh) = π((5/3)r^2 +956/r) , solve dS/dr = 0 ----> r = 1.88 ft and S = ...
