How can we explain why you were wrong when you have not even given us an outline of your working ?
h = 300/ (pi r^2) → h^2 = (90000/ pi^2)r-4
Subbing x for r we have that
S = (pi * x) ( x^2 + (90000/pi^2)x-4 )1/2
The Calculus is messy but this graph shows that there is no x = r that will produce a max.....only a min
A radius of ≈ 4.07 cm will produce a minimum surface area of ≈ 90.229 cm^2
h = 300 / ( pi * 4.072) ≈ 5.76 cm