Question

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

• A. 2hr
• B. 3hr
• C. 4hr
• D. 1hr

Answer 1

Answer: (A)

2hr

Let the level of water in the tank will rise by $7$ cm in $xhrs$

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

$\therefore$ Its length in $x$ hrs $=5x=5000x$metres 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 $xhrs$

$=\pi r^{2}h$

$=\frac{22}{7}\times {\left(\frac{7}{100}\right)}^2\times 5000x$

$=77x{m}^3$

Vol. of water that falls into tank

$=50\times 40\times \frac{7}{100}{m}^3$

$=154m^3$

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

$\Rightarrow 77x=154$

$\therefore x=\frac{154}{77}=2hr$.