Question

Water is flowing at the rate of 3km/hr through a circular pipe of 20 cm internal diameter into a circular cistern of diameter 10 m and depth 2m. In how much time will the cistern be filled.

Answer 1

Hint: In this question time taken to fill the cistern will be the ratio of volume of cistern and the volume of water coming out of the pipe in one hour, and we know that volume of the cylinder is given as $\pi {r^2}h$.

Complete step-by-step answer:
The cistern is in cylindrical shape.
Volume of a cylinder = $\pi {r^2}h$
Radius of cistern $ = \dfrac{{10}}{2} = 5m$
Hence, volume of the cistern $ = \pi \times 5 \times 5 \times 2{m^3}$
Radius of pipe
$
   = \dfrac{{20}}{2}cm = 10cm = \dfrac{{10}}{{100}}m \\
   = \dfrac{1}{{10}}m \\
$
Since the pipe is cylindrical in shape,
Volume = $\pi {r^2}h$
Here, height is considered as the distance traveled = $3km = 3000m.$
Hence, volume of water coming out of pipe in one hour = $\pi \times {\left( {\dfrac{1}{{10}}} \right)^2} \times 3000{m^3}$
Now, time taken to fill the cistern =
$
   = \dfrac{{{\text{Volume of the cistern}}}}{{{\text{Volume of water coming out of pipe in one hour }}}} \\
   = \dfrac{{\pi \times 5 \times 5 \times 2}}{{\pi \times \dfrac{1}{{10}} \times \dfrac{1}{{10}} \times 3000}} \\
   = \dfrac{5}{3}hours \\
   = 1{\text{ }}hour + \dfrac{2}{3}hour = 1{\text{ }}hour + \dfrac{2}{3} \times 60\min \\
   = 1{\text{ }}hour{\text{ 40 minutes}} \\
$

Note: In order to solve these types of problems, first of all remember the formula of all the shapes. Second the height of the pipe is given as the rate of flowing water which we treated as height to solve the problem. Because the amount of water flowing through the pipe in one hour is given as km/ hr. So, if we consider it for one hour the water forms a circular cylinder of radius 10 cm and height 3000m for the above problem. So taking this logic we solved the above problem.