The ratio of the volumes of two cylinders A and B is x : y and the ratio of their heights is a : b. What is the ratio of their radii? 

\(\sqrt {xb}\) : \(\sqrt {ya}\)

Ratio of volumes  = \(\pi \)r₁²h₁    :    \(\pi \)r₂²h₂

                             =           x    :    y .... (i)

Ratio of heights  =  a    :   b

ATQ,

⇒   \(\frac{x}{y}\) = \(\frac{r_1^2 a}{r_2^2 b}\)

⇒ \(\frac{r_1}{r_2}\) = \(\sqrt{\frac{xb}{ya}}\) = \(\sqrt {xb}\) : \(\sqrt {ya}\)