In a hospital used water is collected in a cylindrical tank of diameter $ 2 \mathrm{~m} $ and height $ 5 \mathrm{~m} $. After recycling, this water is used to irrigate a park of hospital whose length is $ 25 \mathrm{~m} $ and breadth is $ 20 \mathrm{~m} $. If tank is filled completely then what will be the height of standing water used for irrigating the park?
Given:
In a hospital used water is collected in a cylindrical tank of diameter \( 2 \mathrm{~m} \) and height \( 5 \mathrm{~m} \).
After recycling, this water is used to irrigate a park of hospital whose length is \( 25 \mathrm{~m} \) and breadth is \( 20 \mathrm{~m} \).
The tank is filled completely.
To do:
We have to find the height of standing water used for irrigating the park.
Solution:
Diameter of the cylinder $d= 2\ m$
This implies,
Radius of the cylinder $r = 1\ m$
Height of the cylinder $H = 5\ m$
Volume of the cylindrical tank $V_1 = \pi r^2H$
$= \pi \times 1^2 \times 5$
$= 5\pi\ m$
Length of the park $L = 25\ m$
Water from the tank is used to irrigate the park.
This implies,
Volume of the cylindrical tank $=$ Volume of the water in the park
$5 \pi = 25 \times 20 \times h$
$h=\frac{5 \pi}{25 \times 20}$
$h = \frac{\pi}{100}\ m$
$h = 0.0314\ m$
The height of standing water used for irrigating the park is $0.0314\ m$.
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