The correct option is B 1:1
Let r be the base radius and h be the height of the cylinder.
Then, 2πrh+πr2=100
⇒h=50πr−r2
Volume of cylinder, V=πr2h=πr2(50πr−r2)=50r−πr32
dVdr=50−3πr22
dVdr=0
⇒r=10√3π
d2Vdr2=−3πr<0 at r=10√3π
Hence, V is maximum when r=10√3π
∴h=50π⋅10√3π−102√3π=10√3π
So, when V is maximum, r:h=1:1