Question

In a hospital, used water is collected in a cylindrical tank of diameter $2m$ and height $5m.$ After recycling, this water is used to irrigate a park of the hospital whose length is $25m$ and breadth is $20m.$ If the tank is filled completely then what will be the height of standing water used for irrigating the park? Write your views on the recycling of water.

Answer 1

Given: Diameter of cylinder $\left(d\right)=2m$
Radius of cylinder $\left(r\right)=1m$
Height of cylinder $\left(H\right)=5m$
Volume of cylindrical tank, $V_c=\pi r^{2}H=\pi \times 1^2\times 5=5\pi m^3$
Length of the park $\left(l\right)=25m$
Breadth of park $\left(b\right)=20m$
Let the height of standing water in the park be ${}^{\prime }{h}^{\prime }$​
The volume of water in the park (Cuboidal in shape) $=l\times b\times h=25\times 20\times h$
Now water from the tank is used to irrigate the park.

So, The volume of cylindrical tank = Volume of water in the park
$\Rightarrow 5\pi =25\times 20\times h$

$\Rightarrow \frac{5\pi }{25\times 20}=h$

$\Rightarrow h=\frac{\pi }{100}$

$\Rightarrow h=0.0314m$ [$\because \pi =3.14$]
Through recycling of water, better use of the natural resource occurs without wastage. It helps in reducing and preventing pollution.
It thus helps in conserving water. This keeps the greenery alive in urban areas like in parks, gardens, etc.