water flows at the rate of 10m/min through a cylindrical pipe 5mm in diameter how long would it take to fill a conical vessel whose diameter at the surface is 40cm and depth is 24cm
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firstly volume of pipe is to be taken out it comes 62.5pi cc then volume of cone it comes 3200pi then divide volume of pipe and cone .in pipe consider rate of flow as height in cm I.e 1000cm
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Answer: 51 minutes and 12 seconds
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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