Question

A conical vessel with base radius $10cm$. contains some water in it. The water level in the vessel is $18cm$ high. It is pored into another cylindrical vessel with a radius $5cm$. Find the water level in the cylindrical vessel.

Answer 1

Base radius of conical vessel $\left(R\right)=10cm$
And the height $\left(H\right)=18cm$
Volume of conical vessel $=\frac{1}{3}\pi R^{2}H$
$=\frac{1}{3}\times \pi \times (10{)}^2\times 18$
$=\pi \times 100\times 6$
$=600\pi {cm}^3$
Let the water lavel in the cylindrical vessel be h.
Radius $\left(r\right)=5cm$
Now according to the problem Volume of water in the cylindrical vessel = Volume of water in conical vessel
$\pi r^{2}h=600\pi$
or $r^{2}h=600$
$\Rightarrow (5{)}^{2}h=600$
$\Rightarrow 25h=600$
$h=\frac{600}{25}$
$=24cm$
Hence the water level in the cylindrical vessel $=24cm$.