Question

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

Answer 1

Diameter of cylinder (d) = 2 m
Radius of cylinder (r) = 1 m
Height of cylinder (H) = 5 m
Volume of cylinderical tank, V_c = \[\pi r^2 H\] 

\[\pi \times \left( 1 \right)^2 \times 5 = 5\pi m\]

Length of the park (l) = 25 m
Breadth of park (b) = 20 m
height of standing water in the park = h​
Volume of water in the park = lbh = \[25 \times 20 \times h\] 

Now water from the tank is used to irrigate the park. So, Volume of cylinderical tank = Volume of water in the park 

\[\Rightarrow 5\pi = 25 \times 20 \times h\]
\[ \Rightarrow \frac{5\pi}{25 \times 20} = h\]
\[ \Rightarrow h = \frac{\pi}{100} m\]
\[ \Rightarrow h = 0 . 0314 m\]