Question

A cylindrical water tank of diameter 2.8 m and height 4.2 m is being fed by a pipe of diameter 7 cm through which water flows at the rate of 4 m/s. Calculate in minutes the time it takes to fill the tank?
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Answer 1

Required answer is = 28 minutes.

Some steps :

• Firstly calculate the volume of cylindrical tank.

• Then calculate the volume of pipe in such a way that height taken is - "H" m.

• Equate both the volumes and get the height of pipe.

• Then divide the obtained height by 4×60.

Answer 2

Given :---

• Diameter of cylindrical tank = 2.8m
• Height of cylindrical tank = 4.2m
• Diameter of pipe = 7cm .
• speed of water = 4m/sec .

Concept used :--

• volume of cylinder = πr²h
• Radius = Diameter /2
• (100)³cm = (1)³m .
• Pipe is in the shape of a cylinder .
• 60 seconds = 1 minute .

Solution :----

→ radius of cylindrical tank = 2.8/2 = 1.4m

Putting values we get,

→ Volume of cylinder = [ π(1.4)²*4.2 ] m³

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Now, let Length of cylindrical Pipe , that is actually its Height, is H .

→ Radius of pipe = 7/2 cm .

→ Volume of pipe = [ π * (7/2)² * H ] cm³

or,

→ Volume of pipe = [( π * (7/2)² * H )/ 100³ ] m³

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Now, since pipe is filling the tank completely , the water that goes from pipe and fill the tank will be Equal .

or, we can say that their volume will be Equal ...

Comparing Their volume now we get,

→ [ π(1.4)²*4.2 ] m³ = [( π * (7/2)² * H )/ 100³ ] m³

( π cancel from each side ) .

→ (1.4*1.4*4.2)*4*100*100*100 = 49* H

→ H = ( 1.96*16.8*100*100*100/49 )

Solving This ( By dividing 7 two times ) we get,

→ H = 6720 m .

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Now, we will understand first what is this 4m/sec.

→ it means that, in sec , 4m of water is running through pipe, so we can say that, in 1 sec . the water is covering a distance of 4m.

→ 4m distance = 1 sec .

→ 1m distance = (1/4) sec.

→ 6720m distance = (1/4) * 6720 = 1680 seconds .

Now, we know that,

→ 60 seconds = 1 minutes .

→ 1 second = (1/60) min.

→ 1680 seconds = (1/60) * 1680 = 28 minutes .

∴ Total time taken at the speed of 4m/sec is 28 minutes .

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★★Extra Brainly Knowledge★★

✯✯ Some Formula of Cylinder ✯✯

→ Curved surface Area of cylinder = 2πrh .

→ Base Area of cylinder = πr²

→ Both Side base Area of cylinder = 2(πr²)

→ Total Surface Area of cylinder = curved surface Area + both side base Area = 2πrh + 2πr² = 2πr ( h + r) ..