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

The volume of a conical flask is $V=\frac{1}{3}\pi r^{2}h$
, where r is the base radius and h is the height of the conical flask.

The water is poured in to a cylindrical flask.

Therefore volume of the conical flask is equal to the volume of the cylindrical flask with a base radius of 'mr'

We need to find the height of the cylindrical flask.

Let H be the height of the cylindrical flask.

The volume of the cylindrical flask is $V=\pi (mr{)}^{2}H$

Equate both the volumes, we have

$\frac{1}{3}\pi r^{2}h=\pi (mr{)}^{2}H$

$\frac{1}{3}{r}^{2}h=m^2{r}^{2}H$

$\frac{1}{3}h=m^{2}H$

$H=\frac{h}{3m^2}$

Thus, the height of the cylindrical flask is $H=\frac{h}{3m^2}$

Hence required height

$H=\frac{h}{3m^2}$