Question 47

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cyclindrical tank, the radius of whose base is 60 cm. By how much will the level of water rise in 30 minutes?

Solution

Rate of flow of water in in the pipe = $$\pi r^{2} h_{1}$$

Where, r = 1 cm, h = 6 m (or) 600 cm

$$\therefore$$ Rate of flow of water in the pipe = 600 $$\pi$$ cm$$^{3}$$/second (or) 600 x 60 $$\pi$$ cm$$^{3}$$/minute

And Water after 30 minutes = 600 x 60 x 30 $$\pi$$ cm$$^{3}$$/minute.........(1) 

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

Where, r = 60 cm, h = ?

$$\therefore$$ Volume of water flown in the tank =  3,600 $$\pi$$ h cm$$^{3}$$......(2)

Equate (1) and (2) as the volume of water in the pipe will be equal to volume of water in tank

600 x 60 x 30 $$\pi$$ = 3,600 $$\pi$$ h

h = 300 cm (or) 3 m

Hence, option C is the correct answer.


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