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प्रश्न
Water flows at the rate of 10 meters per minute through a cylindrical pipe having its diameter 20 mm. how much time will it take to fill a conical vessel of diameter 40 cm and depth 24 cm?
उत्तर
For the cylindrical pipe:
diameter = 20 mm
∴ radius = ` "diameter"/2 = 20/2` = 10 mm = 1cm
Rate of flow of water through the pipe = 10m/minute
= 10 × 100 cm /minute
= 1000 cm/minute
∴ Water flow's through a distance (h) of 1000 cm in a minute
volume of water flowing through the pipe in 1 minute = `pir^2h`
= π × 1× 1× 1000
= 1000π cm3
For the conical vessel:
diameter = 40 cm
∴ radius =`"diameter"/2 = 40/2 = 20` cm
depth (h) = 24cm
Volume of conical vessel = `1/3 pi r^2h`
`= (1/3xx pi xx 20 xx20xx24)` cm3
Time is taken to fill the conical vessel =`" volume of conical vessel"/"volume of water flowing through a pipe in 1 min"`
`= (1/3 xx pi xx 20xx20xx24)/(1000pi)`
`= (pi xx 20xx20xx24)/(3xxpixx1000)`
`= 3200/1000 = `3.2 minutes
∴ Time taken to fill the conical veseel is 3.2 minutes.
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