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Question
Water flows at the rate of 10 metre per minute 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?
Options
48 minutes 15 sec
51 minutes 12 sec
52 minutes 1 sec
55 minutes
Solution
The radius of cylindrical pipe
r = 5/2 mm = 0.25 cm
The volume per minute of water flow from the pipe
`=pi xx (0.25)^2 xx 1000`
`=62.5 pi cm^3`/minute`
The radius of cone
`=40/2`
`=20 cm`
Depth of cone = 24 cm
The volume of cone
`=1/3pi (20)^2 xx 24`
`= 3200 pi cm^3`
The time it will take to fill up a conical vessel
`=(3200pi)/(62.5pi)`
`=51 125/625 min`
`=51 min +125/625 xx 60 sec `
`=51 min + 12 sec`
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