Question

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 6 km/h., in how much time will the tank be filled?

Answer 1

Step by step expln

Radius of the pipe r = 10 cm = (10/100)m = 1/10

length of water flowing through the pipe in 1 hrs.

h = 6km = 6000m

volume of water that flows through the pipe in 1 hrs.

pir*2h = ( pi × 1/10 × 1/10 × 6000)

= 60pi m^3

radius of cylind tank R = 5m

depth of the tank H= 2m

volume of the tank = pir^2H

= (pi×5×5×2) =( 50pi)m^3

time takn to fill the tank

= volume of the tank/ volume of water flown in 1 hrs

= (50pi/60pi) hrs = 5/6 hrs

Hope its hlp ful for uu

Answer 2

Given that the water is flowing at the rate of 5 km/hr through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44m wide.

Let the level of the water in the tank rise by 7 cm in x hours.

Again the water is flowing at the rate of 5 km/hrSo, the length of the

So, the length of the water in x hours = 5x km = 5x * 1000 = 5000x m

Here, the water forms a cylinder having radius r = 14/2 = 7 cm = 7/100 m

and length h = 5000x m

Now, the volume of the water flowing through the cylindrical pipe in x hours = πr2 h

= (22/7)*(7/100)2 *5000x

= (22*7*7*5000x)/(7*100*100)

= (22*7*5x)/10

= (22*7*x)/2

= 11*7*x

= 77x

Now, volume of the water that falls into the tank in x hours = (50*44*7)/100 = (44*7)/2 = 22*7 = 154

Now, volume of the water flowing through the cylinder pipe in x hours = volume of the water that falls in the tank in x hours

=> 77x = 154

=> x = 154/77

=> x = 2

So, the level of water in the tank will rise by 7 cm in 2 hours.