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Question

Water flows at the rate of 10 metres per minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter art the surface 40 cm and depth 24 cm?


Solution

Radius of the cylindrical pipe = 2.5 mm = 0.25 cm
Water flowing per minute = 10 m = 1000 cm
Volume of water flowing per minute through the cylindrical pipe = π(0.25)21000 cm3 = 196.4 cm3
Radius of the the conical vessel = 40 cm
Depth of the vessel = 24 cm
Volume of the vessel = 13π(20)224=10057.1 cm3
Let the time taken to fill the conical vessel be x min.
Volume of water flowing per minute through the cylindrical pipe × x = volume of the conical vessel
x=10057.1196.4=51 min 12 sec
∴ The cylindrical pipe would take 51 min 12 sec to fill the conical vessel.

Mathematics
RS Aggarwal (2017)
Standard IX

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