Question

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 4 km/hour, in how much time will the tank be filled completely?

Answer 1

Let the length of the pipe is h cm. 

Given that internal diameter of pipe is 2r = 20cm. 

∴ Internal radius of pipe is r = \(\frac{20}{2}\) cm = 10cm. 

And height (depth) of the cylindrical tank is H = 2m = 200cm. 

& radius of the cylindrical tank is R = \(\frac{10}{2}\) m 

= 5m 

= 500cm. 

∴ The volume of the cylindrical tank = πR²H

= π × (500)² × 200 

= π × 25 × 2 × 10⁶ 

= 5π × 10⁷cm³. 

And the volume of the pipe = πr²h 

= π × 10²× h 

=10²hπ cm³. 

Since, 

Cylindrical tank is filled by the water which flows through the pipe 

∴ The volume of the pipe = The volume of the cylindrical tank 

∴ 10²hπ = 5π × 10⁷h 

h = \(\frac{5\times 10^7}{10^2}\) 

= 5 × 10⁷⁻² 

= 5 × 10⁵ cm 

= 5 × 10³m 

= 5km. 

(∵ 1km = 1000m = 10⁵cm) 

∴ Length of the pipe is 5km. 

Now, 

Since, 

Water flows in 1 hour through the pipe = 4km. 

∴ Water flows 4 km in pipe in 1 hour.

∴ Time required for flowing 5 km in pipe = \(\frac{1}{4}\) × 5 hour 

= \(\frac{1}{4}\) × 5 × 60 minutes 

= 75 minutes. 

So, in 75 minutes the tank will be filled completely.