Question

A farmer connects a pipe of internal diameter 20 cm from the canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the rate of 3 km/h, in how much time will the tank be filled?

Answer 1

Given:

For the Cylindrical Tank:

Diameter of the tank = 10 m

Radius of the tank (R) = `10/2` = 5 m

Depth/Height of the tank (H) = 2 m

For the Pipe:

Internal diameter of the pipe = 20 cm

Radius of the pipe (r) = `20/2`

= 10 cm

= `10/100` m

= 0.1 m

Rate of water flow (Speed) = 3 km/h = 3 × 1000 m/h

= 3000 m/h

1. Find the Volume of the Tank:

Volume of the cylindrical tank = πR²H

= π × (5)² × 2

= π × 25 × 2

= 50π m³

2. Find the Volume of water flowing through the pipe in 1 hour:

The length of the water column (h) in 1 hour = 3000 m

Volume of water in 1 hour = πr²h

= π × (0.1)² × 3000

= π × 0.01 × 3000

= 30π m³

3. Calculate the Time taken to fill the tank:

Time taken = `"Total volume of the Tank"/"Volume of water flowing in 1 hour"`

= `(50π)/(30π)` 

= `50/30`

= `5/3` hours

4. Convert hours into minutes:

Time = `5/3 xx 60` minutes

= 5 × 20

= 100 minutes