Design a closed cylindrical container $($both the top and the bottom faces are included$)$ which holds $100c{m}^3$ and has the minimal possible surface area. What should its dimensions be$?$

Do this problem in two different ways:

$(5$ points$)$ Treat it as a Calc AB problem.

$(5$ points$)$ Use the method of Lagrange Multiplier.

You must solve the problem with the indicated method in order to receive full credit.