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 44 m wide. Determine the time in which the level of the water in the tank will rise by 7cm.

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5

hours

2

hours

8

hours

3

hours

answer is B.

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Detailed Solution

Given data:
Water is flowing at the rate 5Km/hr. through a pipe of diameter 14cm.
So the length of the cylindrical pipe is, h = 5Km = 5000m, as,

1 k m = 1000 m

And radius is half of the diameter, so

r = d 2 = 142 = 7 c m = 0.07 m

Now as we know that the volume of the cylinder is

π r 2 h

cubic units where symbols have the usual meaning.
So the volume (

V 1

) of the cylindrical pipe =

V 1

⇒ 227 (0.07) 2 (5000) = 77 m 3

So the amount of water that flows out of the cylindrical pipe per hour = 77 cubic meters/hour.
Now the water will flow into the rectangular tank.
Therefore, the amount of water that flows out of the cylindrical tube per hour into the rectangular tank should be the same.
Let the time taken for the water level in the tank to rise by 7 cm be t hours.
Thus, t multiplied by the volume of the cylinder = the volume of the rectangular tank, i.e. the cuboid.

⇒ t × V 1 = V 2 .......... (1)

Now, as we know, the volume of a cuboid is LBH, where the symbols have their usual meaning.
Now given that the rectangular tank is 50 m long and 44 m wide.
So L = 50 m and B = 44 m.
Now the water in the tank will rise by 7 cm = 0.07 m.
So H = 0.07 m.
So the volume