solving for h from the Volume equation

plugging that into the Surface Area equation

now plug in the fact that V=375 ml

now go to wolframalpha.com (or use your favorite graphing software) to plot this expression for the Surface area.

Put "Plot[2 pi r^2 + 750/r,{r,2,6}]" into wolframalpha.com to get a plot.

see if you can take it from here.