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. 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 or tne height ro investigate the sensitivity of the solution by plotting V versus r I-low much can R vary about its optimal value before the area increases 10 percent above its minimum value?

V v= 3 2h A = ur\p2 + h mr