Water flows at the rate of 10m per minute through cylindrical pipe havingirs diametre 20mm how much time will it take to fill a conical vessel of base diametre 30cm and depth 24cm
Answers
≡QUESTION≡
Water flows at the rate of 10 m per min. from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
║⊕ANSWER⊕║
Radius of the pipe = 5/2 mm
= 5/2 x 1/10 cm
= 1/4 cm
Speed of water = 10 m/min
= 1000 cm/min
Volume of water that flows in 1 minute = Π r²h
= 22/7 x 1/4 x 1/4 x 1000
= 1375/7 cm³
Radius of conical vessel = 40/2 = 20 cm
Depth = 24 cm
Therefore, Capacity of the vessel = 1/3 x Π r² h
= 1/3 x 22/7 x 20 x 20 x 24
= 70400/7 cm³
∴ Time required to fill the vessel = capacity of the vessel / volume of water flowing per minute
= 70400/7 / 1375/7
= 70400/7 x 7/1375
= 256/5 minutes
= 51 min 12 sec
∴The time taken is 51 min 12 sec