Question

water flows at the rate of 10mper minute through cylindrical pipe having its diameter 20mm. How much time will it take to fill a conical vessel of base of diameter 40cm and depth 24cm?​

Answer 1

Question:

Water flows at the rate of 10m per minute through cylindrical pipe having its diameter 20mm. How much time will it take to fill a conical vessel of base of diameter 40cm and depth 24cm.

Answer:

3.2 min or 3 min 12 sec

Note:

• 1m = 100 cm

• 1m = 1000 mm

• 1cm = 10 mm

• 1 hr = 60 min

• 1 min = 60 sec

• Radius = Diameter / 2

• Volume of cylinder of radius R and height H is given as ; V = π•R²•H

• Volume of cone of radius R and height H (or depth) is given as ; V = (1/3)•π•R²•H

Solution:

We have,

• Diameter of cylindrical pipe = 20mm

• Radius of pipe = (20/2)mm = 10mm

• Rate of flow of water from the cylindrical pipe

= 10m/min

= (10•1000)mm/min

= 10000mm/min

Note : Here the distance travelled by the water per min can be considered as its height.

Thus,

The volume of water coming out from the pipe

= π•(10)²•10000

= π•(100)•(10000)

= π•1000000 mm³ ------(1)

Now,

• Diameter of conical vessel = 40cm = 400mm

• Radius of vessel = (400/2)mm = 200mm

• Depth of vessel = 24cm = 240mm

Now,

Volume of conical vessel

= (1/3)•π•(200)²•240

= (1/3)•π•40000•240

= π•40000•80

= π•3200000 mm³

From eq-(1) , we can say that ;

=> Time taken to fill π•1000000 mm³ = 1 min

=> Time taken to fill 1 mm³ = 1/π•1000000 min

=> Time taken to fill π•3200000

= π•3200000/π•1000000 min

= 32/10 min

= 3.2 min

= 3 min 12 sec

Hence,

The time required to fill the vessel is 3.2 min or

3 min 12 sec .

Answer 2

Given :---

• Speed of water flows = 10m/min
• diameter of cylindrical pipe = 20mm
• Diameter of conical vessel = 40cm.
• Depth(or height of vessel) = 24cm.

To Find :---

• In how much time conical vessel will fill ?

Formula used :---

• volume of cylinder = πr²h
• Volume of cone = 1/3(πr²h)
• 1m = 100cm = 1000m
• 1cm = 10mm
• 1 hour = 60min .
• 1 min = 60 sec.
• Radius = Diameter /2

Solution :-----

water flows at the rate of 10m/min through cylindrical pipe means that, this is the Height of pipe , ( Length = Height Here) .

So,

→ Height of cylindrical Pipe = 10m/min = 10*1000= 10000mm/min

→ Radius of cylindrical pipe = 20/2 = 10mm .

Putting values in Formula now we get,

→ Volume of cylindrical Pipe = π(10)²*10000 = π*1000000 mm³

_____________________________

Now,

→ Radius of conical vessel = 40/2 = 20cm = 200mm

→ Height of conical vessel = 24cm = 240mm

Again Putting values now in formula we get,

→ Volume of conical vessel = 1/3*π*(200)²*240 = 3200000*π (mm³)

______________________________

Now, Time to Fill conical vessel = Volume of Conical vessel/ volume of pipe flows per min .

→ Time = (3200000*π)/(π*1000000)

→ Time = 32/10 min ..

→ Time = 3min + 2/10 min

→ Time = 3min + (2/10)*60

→ Time = 3 min + 12 seconds .

Hence, Time to Fill the conical vessel is 3 min , 12 seconds .

______________________________

★★Extra Brainly Knowledge★★

✯✯ Some Mensuration Formula ✯✯

→ CSA of cylinder = 2πrh

→ Both Base Area of cylinder = 2πr²

→ TSA of cylinder = CSA + both Base Area = 2πrh + 2πr² = 2πr(h+r)

→ CSA of cone = πr*l ( l = slant Height)

→ l(slant Height of cone) = √(r²+h²)

→ TSA of cone = CSA + Base Area = πrl + πr² = πr(l+r) .