Surface Area

I got really into finding the solution to my cylinder problem from about a month ago. I make numerous equations and quintuple checked my work. It appears to me that the place to cut a cylinder to have a maximum surface area is from the edge of one base to the edge of the other. I thought it would have been slightly inside the edge but it doesn't appear to be true. I'm am actually disappointed at the blandness of my answer. I can only hope that one of my initial equations is wrong.

...okay, I started playing a few parameter and i think i did something wrong. Thank god it's not bland anymore. I can go crazy again!