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  • Water is flowing at the rate of 5 km/hour through a pipe of diameter 14 cm into a rectangular tank,which is 50 m long and 44 m wide.Determine the time in which the level of water in the tank will rise by 7 cm.

Water is flowing at the rate of 5 km/hour through a pipe of diameter 14 cm into a rectangular tank,which is 50 m long and 44 m wide.Determine the time in which the level of water in the tank will rise by 7 cm.

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Let the level of water in the tank will rise by 7 cm in x hrs


As the rate of flow of water is 5km/hr.


∴ Its length in x hrs =5x=5000xmetres Water column forms a cylinder whose radius is

\\ \Rightarrow r=\frac{14}{2} cm =\frac{7}{100} m$ \\ Volume of water flowing through the cylindrical pipe in $x$ hrs \\ $=\pi r^{2} h$ \\ $=\frac{22}{7} \times\left(\frac{7}{100}\right)^{2} \times 5000 x$ \\ $=77 x m^{3}$ \\ Vol. of water that falls into tank \\ $=50 \times 40 \times \frac{7}{100} m^{3}$ \\ $=154 m^{3}$

But, the volume of water flowing through the cylindrical pipe in x hrs = Vol. of water that falls in a tank in x hrs.

\begin{array}{l} \Rightarrow 77 x=154 \\ \therefore x=\frac{154}{77}=2 h r \end{array}

Posted by

Deependra Verma

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