Question

a farmer connects a pipe of internal diameter 20 cm from a canal into cylindrical tank which is 8 metre in radius and 4 metre deep water flow through the pipe @ 8 kilometre per hour in how much time will the tank will be filled

Answer 1

$\huge{\text{\underline{Correct\:Question}}}$

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

$\huge{\text{\underline{Solution}}}$

★Using formula:-

$\huge{\sf{\boxed{\boxed{Volume\:of\:cylindrical\:tank\:{= \pi r^2h}}}}}$

$\implies$ 22/7 × 10/2 × 10/2 × 2

$\implies$ 1100 / 7 m³

★ Given:-

• Radius of pipe = 10 cm = 0.1 m

• Speed = 4 km/h = 4000m/h

★ Explanation:-

Let length of water column be 'x' meter.

Volume of water column = 1100/7 m³

$\implies$ πr²h

$\implies$ 22/7 × 0.1 × 0.1 × x

$\implies$ 0.22x / 7

$\implies$1100 / 7 = 0.22x / 7

$\implies$1100 = 0.22x

$\implies$1100 / 0.22 = x

$\implies\sf{\boxed{x = 5000}}$

Therefore, length of water column = 5000 m = 5km.

$\implies$ Time = Distance / Speed

$\implies$Time = 5 / 4

$\implies\sf{\boxed{Time = 1.25 hrs}}$

Therefore the time taken to fill the tank completely is 1 hours and 15 minutes.

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Answer 2

AnswEr :

• Radius of Pipe = 20 cm/2 = 10 cm
• Cylindrical Tank Radius = 8 m
• Cylindrical Tank Height = 4 m
• Rate of Water Flow = 8 km/hr

Radius of Pipe = 10 cm = 10/100 m = 1/10 m

Rate of flow of water = 8 km/h = 8000 m/h

Let the time taken be t hr to fill up tank.

• Volume of the water that flows in t hour :

⇒ Area of Cross Section × Speed × Time

⇒ πr² × Speed × Time

⇒ π × ( 1 /10 )² × 8000 × t

⇒ π × 1 /100 × 8000 × t

⇒ π × 80 × t

⇒ 80πt

• Volume of Cylindrical Tank :

⇒ πr²h

⇒ π × ( 8 )² × 4

⇒ π × 64 × 4

⇒ 256π

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• Now we will calculate time taken :

⇝ Vol. of water flows in t hr = Vol. of Tank

⇝ 80πt = 256π

• Dividing Both term by 8π

⇝ 10t = 32 hr

⇝ t = 32 /10 hr

• Changing it into minutes

⇝ t = 32 /10 × 60 minutes

⇝ t = 32 × 6 minutes

⇝ t = 192 minutes

⇝ t = 3 hr. 12 minutes

∴ Time taken will be 3 hr and 12 minutes.