The volume V and paper surface area A of a conical paper cup are given by V = (1/3)r 2 h A = r(r 2

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

V = (1/3)πr ² h A = πr√(r ² + h ² )

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

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

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.

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?