The ratio of the volumes of two right circular cylinders A and B is $$\frac{x}{y}$$ and the ratio of their heights is a : b. What is the ratio of the radii of A and B?

Volumes of two right circular cylinder = $$\pi r^2 h$$

The ratio of the volumes of two right circular cylinders A and B = $$\frac{x}{y}$$

let the r1 and r2 be the radius of two right circular cylinders A and B.

$$\frac{\pi (r1)^2 h}{\pi (r2)^2 h} = \frac{x}{y}$$

$$\frac{\pi (r1)^2 a}{\pi (r2)^2 b} = \frac{x}{y}$$

$$\frac{r1}{r2}  =\sqrt{\frac{xb}{ya}}$$

The ratio of the radii of A and B = $$\sqrt{\frac{xb}{ya}}$$