The radii of two cones are in the ratio 2 : 1

Let the radius of the first cone = 2x

And height of the first cone = h1

Then,

Volume of the first cone $=\frac{1}{3} \pi r^{2} h$

$=\frac{1}{3} \pi(2 x)^{2} h_{1}$ ......(i)

      The radius of the second cone = x

Height of the second cone = h2

Then,

Volume of the second cone $=\frac{1}{3} \pi r^{2} h$

$=\frac{1}{3} \pi(x)^{2} h_{2}$

Since,

The volumes of the two cones are equal.

Or $h_{1}: h_{2}=1: 4$