5. Use MATLAB for the following question:

The volume V and paper surface area A of a conical paper cup are given by,

V= 1/3hr^2, A=r r^2+h^2

where r is the radius of the base of the cone and h is the height of the cone.

i. By eliminating h, obtain the expression for A as a function of r and V.

ii. 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.

iii. For V= 12 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 8 percent above its minimum value?