# A rectangular water reservoir is 10.8 m by 3.75 m at the base . water flows into it at the rate of 18 m per second through a pipe having the cross section 7.5cm *4.5cm . find the height to which the water will rise in the reservoir in 30 minutes .

Solution : Water that flows into the reservoir in one second forms a cuboid of dimensions $7.5cm \times 4.5cm \times 1800cm.$

$\therefore$  Volume of water that flows in one second

$= (18\times 0.075\times 0.045)m^3 = 18\times \frac{75}{1000}\times \frac{45}{1000}m^3=\frac{243}{4000}m^3$

Volume of the water that flows in 30 minutes   $=$       $\frac{243}{4000}\times 60\times 30 m^3= \frac{2187}{20}m^3$

Area of the base of the reservoir $= (10.8 \times 3.75)m^2$

$\therefore$  Height of water  = volume / Area of the base       $=\frac{2187}{20} \times \frac{1}{10.8\times 3.75}m =2.7m$

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