The ratio of radii of two cylinders is 1:2 and the heights are in the ratio 2:3. The ratio of their volumes is_____.

Given:

The ratio of radii of two cylinders is 1:2 and the heights are in the ratio 2:3. 

To do:

We have to find the ratio of their volumes.
Solution:
Let the radii of the two cylinders be $x$ and $2x$. 

Similarly, let the heights of the two cylinders be $2y$ and $3y$.

We know that,

Volume of a cylinder of radius $r$ and height $h$ is $\pi r^2h$.

Therefore,

The ratio of the volumes of the two cylinders $=\pi (x)^2(2y) : \pi (2x)^2(3y)$

$=2x^2y:12x^2y$

$=2:12$

$=1:6$

The ratio of their volumes is $1:6$.