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.