Question

The $\frac{3}{4}th$ part of a conical vessel of radius $5cm$ and height $24cm$ is full of water. The water is poured into a cylindrical vessel with radius $10cm$. Find the height of water level in cylindrical vessel.

Answer 1

Volume of cone$=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times 3.14\times 5\times 5\times 24$

$=628c{m}^3$

Water filled$=\frac{3}{4}\times 628=3\times 157$

$=471c{m}^3$

This volume of water fills the cylinder

Volume of cylinder$=\pi r^{2}h$

$471=3.14\times 10\times 10\times h$

$\therefore h=\frac{471}{314}=1.5$cm

$\therefore$ Height of water level in cylindrical vessel$=1.5$cm.