Question

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.

Answer 1

Hint: we need to know the formulae for finding the volume of cone and cylinder to proceed further.
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 $H$.
Flask full of water is poured from conical flask to cylindrical flask. We need to find the height of water in the cylindrical flask.
$$ \Rightarrow \frac{1}{3}\pi {r^2}h = \pi {(mr)^2}H$$
$H = \frac{h}{{3{m^2}}}$
$\therefore $The height of water in cylindrical flask is $H = \frac{h}{{3{m^2}}}$
Note: Initially volume of the water is equal to volume of conical flask. Now the water is poured from that conical flask into a cylindrical flask. The height of water in the cylindrical flask is equal to the volume of water.