The ratio of radii of a cylinder to a cone is 3 : 1. If their heights are equal. What is the ratio of their volumes?

27 : 1

The ratio of radii of a cylinder to a cone =  3 : 1

Let radius of the cylinder be r1, and that of cone be r2

⇒ r1 : r2 = 3 : 1

Given, their heights are equal

Ratio of volume of cylinder to cone = ($\pi r1^2h$)  :  ($\frac{1}{3} \pi r2^2h$)

                                                   = ($\pi 3^2h$)  :  ($\frac{1}{3} \pi 1^2h$)

                                                    = 27  :  1 

Thus, the ratio of volume of cylinder to cone = 27 : 1