We have,
Ratio of their height = 1:2
Height of cylinder 1 = h1
Height of cylinder 2 = h2
h1 / h2 = 1/2
Volume of cylinder 1, V1 = volume of cylinder 2, V2
V1 = V2
πr12h1 = πr22h2
r12 / r22 = 2/1
r1 / r2 = √(2/1)
= √2 / 1
∴ Ratio of their radii is √2:1