Question

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/hr, in how much time the tank will be filled?

Answer 1

Heya friend,

We know,

The pipe is of the shape cylinder whereas the tank is cylindrical.

We know,

The volume of the water flowing from the pipe to the tank is equal, or in simple words, the same volume of water passes from the pipe to tank,

So, we get,

Volume of pipe = Volume of tank

Here,

Water from pipe flows at the rate of 3 km / hr by which we get the length of the pipe as

h = 3 km

or, h = 3000 m  

Internal diameter of pipe = 20 cm =  $\frac{20}{100}$ m = $\frac{1}{5}$m

So, internal radius = $\frac{1}{5} * \frac{1}{2} m$

                               =  $\frac{1}{10} m$

and,

diameter of cylindrical tank = 10 m

i.e. , radius = 5 m

Now,

Volume of cylindrical pipe = $\pi r^{2} h$

                                           = $\pi$ * $(\frac{1}{10}) ^{2}$ * 3000

                                           = 30 $\pi$ $m^{3}$

And,

Volume of tank = $\pi r^{2} h$

                         = $\pi$ * $5^{2}$ * 2

                         = 50 $\pi$ $m^{3}$

Now,

We have got top know that the total capacity/volume of the tank is 50 $\pi$ and the volume of water flowing through pipe in an hour is 30 $\pi$

Clearly,

Time taken to fill the tank completely = total volume/capacity of tank / volume of water flowing through pipe in one hour

                                                             = 50 $\pi$ / 30 $\pi$ hrs

                                                            = $\frac{5}{3}$ hrs

                                                             

Now,

1 hour = 60 mins

So,

$\frac{5}{3} hrs$ = $\frac{5}{3}$ × 60 mins

                                     = 5 × 20 mins

                                     = 100 mins or I hour 40 mins {I hour =  60mins + 40mins = 100 mins}                                                        

Thanks,

Manav

Answer 2

Explanation:

R=10 cm

R=500cm

h=200cm

volume of water flows in 1 hr =pie×10×10×300000(cmcube)

volume of cylindrical tank =pie×500×500×200

time taken to be fill the tank=volume of cylindrical tank÷volume of water flow in 1 hr

=(pie×500×500×200)÷pie×10×10×300000

=(5÷3)hr

=(5÷3)×60

=100min

hope it helps u mate

●【answered by shraddhasingh3031】●