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 recycling of water.

Answer 1

Hint: For solving this question you should know about the volume of cylinder and volume of a park shape. So, we will calculate the volume of the cylindrical tank and the park of the hospital and these both are equal, so we compare them to find the height of this park and then we will get the final height for the park.

Complete step-by-step solution:
According to the question we have to find the height of standing water used to irrigate the park when the tank is filled completely and the diameter of the cylindrical tank is 2m and height is 5m. Now, if we calculate the volume of the cylindrical tank, then,
Diameter of cylinder $\left( d \right)=2m$
Radius of cylinder $\left( r \right)=\dfrac{d}{2}=\dfrac{2}{2}=1m$
Height of cylinder $\left( H \right)=5m$
Volume of cylindrical tank,
$\begin{align}
  & {{V}_{c}}=\pi {{r}^{2}}H \\
 & =\pi \times {{\left( 1 \right)}^{2}}\times 5 \\
 & =5\pi {{m}^{3}} \\
\end{align}$
Now if we see the length of the park $\left( l \right)=25m$
Breadth of the park $\left( b \right)=20m$
The height of standing water $=h$
Volume of water in the park $=l\times b\times h=25\times 20\times h$
Now, water from the tank is used to irrigate the park, so,
Volume of cylindrical tank = Volume of water in the park.
$\begin{align}
  & \Rightarrow 5\pi =25\times 20\times h \\
 & \Rightarrow h=\dfrac{5\pi }{25\times 20} \\
 & \Rightarrow h=\dfrac{5\times 22}{50\times 7}=0.0314m \\
\end{align}$
So, the height of the park is 0.0314m.
Through recycling of water, better use of the natural resources occurs without its wastage. It helps in reducing and preventing pollution. It thus helps in conserving water. This keeps the greenery alive in urban areas like parks, gardens etc.

Note: If any type of this question is asked to determine the height, radius, volume, then it will definitely give options for taking the values of that and if that is not given then it will give us any same type of diagram or any shape which will be same in any type of parameter, we can then calculate what is asked of us.