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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 $1:6$.
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