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Water is flowing at the rate of 3 km/hr through a circular pipe of 20 cm internal diameter into a circular cistern of diameter 10 m and depth 2 m. In how much time will the cistern be filled?

(a) 2 hours

(b) 1 hour 40 min

(c) 1 hour 15 min

(d) 2 hour 30 min

1 Answer

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Best answer

Correct option is (b) 1 hour 40 min

Suppose the cistern is filled in x hours. Since water is flowing at the rate of 3km/hr. 

Therefore length of the water column in x hours = 3x km = 3000x metres

Clearly, the water column forms a cylinder of radius

\(r = \frac{20}2 \)cm = 10cm = \(\frac 1{10}\)m

and h = height = 3000x metres

Volume of the water that flows in the cistern in x hours = πr2h

\(= \left(\frac{22}7 \times \frac 1{10} \times \frac 1{10} \times 3000 x\right)\)m3

Also volume of the cister = \(\left(\frac {22}7 \times 5 \times 5 \times 2\right) \)m3

Since the cistern is filled in x hours

Volume of the water that flows in the cistern in x hours = volume of the cistern

⇒ \(\frac{22}7 \times \frac 1{10} \times \frac 1{10} \times 3000 x = \frac {22}7 \times 5 \times 5 \times 2\)

⇒ \(x = \left(\frac{5\times 5 \times 2 \times 10\times 10}{3000}\right)\)hrs 

= 1 hour 40 minutes

∴ Cistern is filled in 1 hour 40 minutes.

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