Water flows at the rate of 10 meters per minute through a cylindrical pipe 5mm in diameter. How long would it take to fill a conical vessel having base diameter of 42cm and depth of 24 cm?
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Answer:
51 min. 12 sec.
Step-by-step explanation
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 r2 h = 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
Therefore, 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
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