Question

The radius and height of a conical vessel are $10cm$ and $18cm$ respectively, which is filled with water to the brim. It is poured in a cylindrical vessel of radius $5cm$.find the height of water level in cylindrical vessel.

Answer 1

Let the radius and height of conical vessel be 'r' and 'h' and that of cylinder be 'R' and 'H' (height upto which water is filled in cylindrical vessel).

Since, same volume of water is transferred to cylindrical vessel,

Volume of conical vessel = Volume of cylindrical vessel

$\frac{\pi r^{2}h}{3}$ $=\pi R^{2}H$

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

$H=$ $\frac{100\times 18}{3\times 25}$ $=24cm$