Let the radius of the cylinder be x cm and the radius of the cone be y cm and the height of both the cylinder and the cone be h cm.

the volume of the cylinder = (πx²h) cm³

the volume of the cone = (1/3) × πy² × h cm³

The volumes of a cylinder and a cone are in the ratio 3 : 1.

Now we can write,

$(\frac{{\pi {x^2}h}}{{\left[ {\;\left( {\frac{1}{3}} \right) \times \;\pi {y^2}\; \times \;h} \right]}} = \frac{3}{1})$

⇒ πx²h = 3 × (1/3) × πy² × h

⇒ x² = y²

⇒ x = y

So, radius of the cylinder and cone are equal.