Question

The rain water from a roof of $22m\times 20m$ drains into a cylindrical vessel having diameter of base $2m$ and height $3.5m$. If the vessel is just full, find the rainfall in cm.

Answer 1

We have
Radius of cylindrical vessel$=r=1m$

Height of cylindrical vessel$h=3.5m$

Volume of cylindrical vessel$=\pi r^{2}h=\frac{22}{7}\times 1^2\times 3.5m^3=11m^3$

Let the rainfall be $x$ cm.

Then volume of the water = Volume of a cuboid of base $22m\times 20m$ and height $x$ metres$=(22\times 20\times x)m^3$

Since the vessel is just full of water that drains out of the roof into the vessel

Volume of the water = Volume of the cylindrical vessel

$22\times 20\times x=11$

$\Rightarrow x=\frac{11}{22\times 20}=0.025m=2.5cm$

$\therefore$ Rainfall$=2.5cm$