Two right circular cylinder of equal volume have their height in the ratio 1:2. What is the ratio of their radii?
Let the two cylinders be with volume V1 and V2 with their respective radii and height as r1, r2 and h1, h2
Now given ratio of their heights i.e. h1:h2 = 1:2
∴ h1/h2 = 1/2
Volume of cylinder = πr2h
Given that volumes of both cylinder are equal i.e. V1 = V2
∴ π × r12 × h1 = π × r22 × h2
h1/h2 = r22/ r12
r22/ r12 = 1/2
r2/r1 = 1/√2
r1/r2 = √2/1
Therefore the ratio of their radii is r1:r2 = √2:1