+129849 I looked at this the other day, jenny....unless I blew a fuse (always possible)....I didn't find any max
Here's what I did
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 positive x = r that will produce a max.....only a min
https://www.desmos.com/calculator/zpyqlutuoq
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
P.S. - check my math....I could have missed something
