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# A conical flask is full of water. The flask has base-radius $r$ and height $h$. The water is poured into a cylindrical flask of base-radius $mr$. Find the height of water in the cylindrical flask.

Last updated date: 29th Mar 2023
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Volume of conical flask with base-radius r and height h is $\frac{1}{3}\pi {r^2}h$
Volume of a cylindrical flask with radius r and height h is $\pi {r^2}h$
Here, it is given that the base radius of the cylindrical flask is $mr$.
Let the Height of water in a cylindrical flask be $H$.
$$\Rightarrow \frac{1}{3}\pi {r^2}h = \pi {(mr)^2}H$$
$H = \frac{h}{{3{m^2}}}$
$\therefore$The height of water in cylindrical flask is $H = \frac{h}{{3{m^2}}}$