The roof of a silo is made by revolving a curve y = 12 cos? (r) from z 0m to z = 4 m about the y axis. The surface area, Sthat is obtained by revolving a curve y = f(z) in the domain from a tob around the y axis can be calculated by: S = 27 zV1+ [F"(x)]dr Calculate the surface area of the roof using: a) Simpson's 1/3 method. Divide the whole interval into eight subintervals. (4 marks) b) Simpson's 3/8 method. Divide the whole interval into nine subintervals. (4 marks)