Surface area S=2πrh+πr2 where h is the cylinder's height.
Volume V=πr2h=100L, so h=100/(πr2), and:
S=2πr(100/(πr2))+πr2=200/r+πr2=(200+πr3)/r.
Note that 1L=1000mL=1000cc=1000cm3=1000×(10-2)3=0.001m3.
For minimum S, dS/dr=0:
-200/r2+2πr=0, -100+πr3=0,
r3=100/π=31.831L approx=31831cm3).
r=31.692cm=0.3169m approx.
This corresponds to a minimum surface area=9466cm2=0.9466m2 approx.