The volume V and paper surface area A of a conical paper cup are given by
where r is the radius of the base of the cone and h is the height of the cone.
a. By eliminating h, obtain the expression for A as a function of r and V.
b. Create a user-defined function that accepts R as the only argument and computes A for a given value of V. Declare V to be global within the function.
c. For V = 10 in.3, use the function with the fminbnd function to compute the value of r that minimizes the area A. What is the corresponding value of the height h? Investigate the sensitivity of the solution by plotting V versus r. How much can R vary about its optimal value before the area increases 10 percent above its minimum value?
