Question

A conical flask is full of water. The flask has base radius $3cm$ and height $15cm$. The water is poured into cylindrical glass tube of uniform inner radius $1.5cm$ placed vertically and closed at lower end. Find the height of water in the glass tube.

Answer 1

Given that:

Radius of conical flask $=3cm$

Height of conical flask $=15cm$

Uniform inner radius of cylindrical glass$=1.5cm$

To find:

The height of water in the glass tube$=?$

Solution:

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

$=\frac{1}{3}\times 3.14\times (3{)}^2\times 15c{m}^3$

$=141.3c{m}^3$

Volume of cylindrical glass $=\pi \times r^2\times h$

$=3.14\times (1.5{)}^2\times h$

$=7.065\times hc{m}^3$

Volume of conical flask $=$ Volume of cylindrical glass

or, $141.3c{m}^3=7.065\times hc{m}^2$

or, $h=20cm$

Therefore, The height of water in the glass tube $=20cm.$