I know how to find the radius and height for minimum surface area. [https://www.physicsforums.com/threads/maximum-surface-area-of-cylinder.332279/ ]. For it to be minimum, h=r/2. It would be great if someone could tell me how to find the values for maximum value.
There is no maximal surface area.
To see that, start with an arbitary cylinder with the given volume.
Then, divide the height by $4$ and double the radius. The volume does not change, but the area of the circle is $4$ times larger.
You can repeat this process as often as you want. It is clear that there is no upper bound for the surface area.