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 $ m r $. Find the height of water in the cylindrical flask.

Given:

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 \( m r \).

To do:

We have to find the height of water in the cylindrical flask.

Solution:

Radius of the conical flask $=r$

Height of the conical flask $=h$ 

This implies,

Volume of the water filled in the flask $=\frac{1}{3} \pi r^{2} h$

Base radius of the cylindrical flask $=m r$

Let the height of the cylindrical flask be $H$.

Volume of the cylindrical flask $=\frac{1}{3} \pi r^{2} h$

According to the question,

Volume of the water filled in the flask $=$ Volume of the cylindrical flask

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

$\Rightarrow \pi(m r)^{2} \times \mathrm{H}=\frac{1}{3} \pi r^{2} h$

$\Rightarrow \mathrm{H}=\frac{1 \times \pi r^{2} h}{3 \times \pi \times m^{2} r^{2}}$

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

The height of water in the cylindrical flask is$\frac{h}{3 m^{2}}$.

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Updated on: 10-Oct-2022

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