A farmer connects a pipe of internal diameter 20 cm from a canal into

1.	A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field which is 10 cm in diameter and 2m deep. If water flows through 3 kmph, in how much time will the tank be filled completely?
Answer» The time required to fill the tank completely is 100 minutes. Step-by-step EXPLANATION: From question, internal DIAMETER of pipe = 20 cm Now, the internal radius of pipe = 10 cm = 10/100 m = 1/10 m From question, the rate of flow of water = 3 km/h = 3000 m/h Let the time required to fill the tank be x Volume of water flowing from pipe = Area of cross SECTION × Speed × Time Volume of water that flows from pipe = πr² × Speed × Time On substituting the known values, we GET, Volume of water that flows from pipe = π(1/10)² × 3000 × x Volume of water that flows from pipe = 30 πt m³ Diameter of the cylinder = 10 m Radius of the cylinder = 5 m Depth of the cylinder = 2 m Volume of tank = πr²h On substituting the known values, we get, Volume of tank = π × (5)² × 2 Volume of tank = 50π m³ Volume of water that flows from pipe = Volume of tank 30 πt = 50π t = 50/30 hours t = 50/30 × 60 minutes Therefore, t = 100 minutes

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

Answer»

Step-by-step EXPLANATION:

From question, internal DIAMETER of pipe = 20 cm

Now, the internal radius of pipe = 10 cm = 10/100 m = 1/10 m

From question, the rate of flow of water = 3 km/h = 3000 m/h

Let the time required to fill the tank be x

Volume of water flowing from pipe = Area of cross SECTION × Speed × Time

Volume of water that flows from pipe = πr² × Speed × Time

On substituting the known values, we GET,

Volume of water that flows from pipe = π(1/10)² × 3000 × x

Volume of water that flows from pipe = 30 πt m³

Diameter of the cylinder = 10 m

Radius of the cylinder = 5 m

Depth of the cylinder = 2 m

Volume of tank = πr²h

On substituting the known values, we get,

Volume of tank = π × (5)² × 2

Volume of tank = 50π m³

Volume of water that flows from pipe = Volume of tank

30 πt = 50π

t = 50/30 hours

t = 50/30 × 60 minutes

Therefore, t = 100 minutes