The ratio of radii of two cylinders is 1:2. If the ratio of their height is 2:1, then what will be the ratio of their volumes?

Given:

The ratio of radii of two cylinders is 1:2 and the ratio of their heights is 2:1. 

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 $y$.

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 $=\pi (x)^2(2y) : \pi (2x)^2(y)$

$=2x^2y:4x^2y$

$=2:4$

$=1:2$

The ratio of their volumes is $1:2$.