The radius of a cylindrical cistern is 10 metres and its height is 15

1.	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» (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.

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»

(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.