Question

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

Answer 1

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

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• A farmer connects a pipe of internal diameter 20 cm form a canal into a cylindrical tank in her field

• Diameter = 10 m

• Height = 2m

• Water flows through the pipe at the rate of 3 km/h

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• Time Taken by the cylindrical tank to be filled

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• Tank will be filled in 100 minutes

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First we need to know about some basic terms before going into answer

• Diameter : The diameter is the length of the line through the center that touches two points on the edge of the circle.

• Radius : The distance from the center of the circle to any point on the circle

Also :

• Diameter = 2 × Radius

• Radius = Diameter/2

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• Here, it is given that the farmer connects the pipe to the cylindrical tank and hence water will flow through the pipe to  fill the tank. We know that the capacity of any solid is known as the volume of that solid. So, we can observe that the  volume of the tank will be equal to the volume of water flowing through the pipe at the time when the tank will be  filled.

Volume of Pipe = Volume of Tank

⇒ Volume of Cylinder = Volume of Tank

⇒ πr²h = Volume of Tank

In the case of : Volume of Pipe

• Height = h
• Diameter = 20 cm

In the case of : Volume of Tank

• Height = 2 m
• Diameter = 10 m

⇒ πr²h = Volume of Tank

Since Radius = Diameter/2

⇒ π × (diameter/2)² × h = Volume of Tank

⇒ π × (20 cm/2)² × h =  πr²h

⇒ π × (20 cm/2)² × h =  π × (diameter/2)² × h

⇒ π × (10 cm)² × h =  π × (10 m/2)² × h

⇒ π × (1/10 m)² × h =  π × (5 m)² × h

⇒ π × 1/100 m² × h =  π × (5 m)² × 2 m

⇒ π/100 m² × h =  π × 25 m² × 2 m

⇒ πh/100 m² =  π × 50 m³

⇒ πh/100 m² = 50π m³

Multiplying both sides by 100 :

⇒ πh/100 m² × 100 = 50π m³ × 100

⇒ πhm² = 50π m³ × 100

⇒ πhm² = 5000π m³

Dividing both sides by πm² :

⇒ πhm²/πm² = (5000π m³ ) /πm²

⇒ h = 5000 m

Since 1000 m = 1 km ⇒ 5000 m = 5 km

⇒ h = 5000 km

Now :

• Water flows through the pipe at the rate of 3 km/h

1 km travel in pipe = 1/3 hour

5 km travel in pipe = 5 × 1/3 hour

⇒ 5 km travel in pipe = 5/3 hour

We know 1 hour = 60 minutes

⇒ 5 km travel in pipe = 5/3 × 60 minutes

⇒ 5 km travel in pipe = 5 × 60/3 minutes

⇒ 5 km travel in pipe = 300/3 minutes

⇒ 5 km travel in pipe = 100 minutes

∴ Tank will be filled in 100 minutes

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Answer 2

Answer:

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In hundred minutes the tank will be filled..

Step-by-step explanation:

let length of pipe for filing hole tank be h m

so,

volume of pipe = volume of tank

Volume of pipe :-

pipe is in form of of cylinder where

let height = h m

diameter = 20cm

so, radius = diameter/2

= 20/2

= 10cm

= 10 × 1/100 m

= 1/10 m

volume of pipe = volume of cylinder

= πr²h

= π(1/100)h

= πh/100

Volume of tank

Tank is in form of cylinder were

Diameter = 10cm

Radius = r = 10/2 m = 5m

Height = h = 2m

Volume of tank = πr²h

= π(5)²×2

= π×25×2

= π×50

= 50π

Now,

Volume of pipe = Volume of tank

πh/100 = 50π

h = 50π×100/π

h = 5000

h = 5km

Now,

water in pipe flows at rate 3km/hr

So,

3km travels in pipe in 1 hour

1km travels in pipe 1/3 hr

5km travels in pipe = 5/3 hour

= 5/3×60 minutes

= 5×20 minutes

= 100 minutes

So, in 100 minutes, the tank will be filled