Water is flowing at the rate of 15 km/hour through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm?
Given: Rate of water flow$=15\ km/h$, diameter of the pipe$=14\ cm$, length of the cuboid$=50\ m$ and width of the cuboid$=44\ m$, rise of water level in the pond.
To do: To find the time to rise the water level 21 cm.
Solution:
Let the level of water in the pond rises by 21 cm in /hours.
Speed of water$=\ 15\ km/hr\ $
Diameter of pipe $=14\ cm=\frac{14}{100} \ m$
Radius of the pipe,$\ r\ =\ \frac{1}{2} \times \frac{14}{100} =\frac{7}{100} \ m$
Volume of water flowing out of the pipe in 1 hour
$=πr^{2} h=\frac{22}{7} \times \left(\frac{7}{100}\right)^{2} \times 15000$
$=\ 231\ m^{3}$
Volume of water flowing out of the pipe in t hours $=\ 231\times t\ \ m^{3}$
Volume of water in the cuboidal pond
$=\ 50\times 44\times \frac{21}{100} \ m^{3} =462\ m^{3}$
Volume of water flowing out of the pipe in t hours = Volume of water in the cuboidal pond
$231\times \ t\ =\ 462$
$\Rightarrow t=\frac{462}{231} =2\ hour$
$\therefore$ In 2 hours the water level in the pond will rise by 21 cm.
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