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 25 m long and 22 m wide. Find the time in which the level of water in the tank will rise by 30 cm

Answer 1

Step-by-step explanation:

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

⇒r=

2

14

cm=

100

7

m

Volume of water flowing through the cylindrical pipe in x hrs

=πr

2

h

=

7

22

×(

100

7

)

2

×5000x

=77xm

3

Vol. of water that falls into tank

=50×40×

100

7

m

3

=154m

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.

⇒77x=154

∴x=

77

154

=2hr.

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Answer 2

We have been given that the water is flowing at the rate of 5km per hour through a pipe of diameter 14cm. Now the volume of water flowing from the pipe is equal to the volume of the tank that needs to be filled. Hence, it takes 2 hours for the level of water to rise by 7cm.