Question

The radius of a cylindrical cistern is 10 metres and its height is 15 metres. Initially the cistern is empty. We start filling the cistern with water through a pipe whose diameter is 50 cm. Water is coming out of the pipe with a velocity 5 m/s. How many minutes will it take in filling the cistern with water? 

(a) 20 

(b) 40 

(c) 60 

(d) 80

Answer 1

(d) 80 min

 Volume of the tank = πr²h = π x (10)² x 15 = 1500π m³

Area of the pipe = \(\frac{πD^2}{4}=\frac{π\times(0.05)^2}{4} = \frac{π}{16}\) m²

Rate of flow of water in the pipe 

= Area × Velocity = \(\frac{π}{16}\times5=\frac{5π}{16}\) m³/s

∴ Time required to fill the tank = \(\frac{1500π}{\frac{5π}{16}}\) seconds

= 4800 seconds = \(\frac{4800}{60}\) min = 80 min.