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Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in a tank in half an hour?

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90 cm

99 cm

98 cm

93 cm

answer is A.

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Detailed Solution

It is given that the water flows through a cylindrical pipe at the rate of

80 c m / sec

.
Converting the half an hour into seconds:

12 hr = 12 × 60 × 60 12 hr = 1800 seconds

The rise in water level:
Let the height of the flowing water be

x

cm. Also, the volume of the water in the cylindrical tank is the same as the volume of water flow from the circular pipe in half an hour.
So,

π r 1 2 h 1 = π r 2 2 h 2

We have,

velocity = distance time ⇒ distance = velocity ​ ​ × ​ ​ time

Distance is the same as the height of the water flow. So,

π r 1 2 h 1 = π r 2 2 v t 40 × 40 × x = 1 × 1 × 80 × 1800 x = 1440001600 x = 90 c m

The rise in the water level in the tank is 90cm in half an hour.
Therefore, 1 is the correct option.

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