The only "plug-in" formulas I can think of are the formulas for volume and surface area of a cylinder: and .
No, I cannot give you "an example such as the volume = 1L" because in your question, it is the surface area that is given, not the volume. I can show how to get the minimum volume given that the surface area is .
With , we can solve for h: . Putting that into the formula for volume, . The extreme (maximum or minimum) values occur where the dervative is 0: or