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प्रश्न
A cylindrical water tank of diameter 2.8 m and height 4.2 m is being fed by a pipe of diameter 7 cm through which water flows at the rate of 4 m s–1. Calculate, in minutes, the time it takes to fill the tank.
उत्तर
Diameter of cylindrical tank = 2.8 m
Therefore, radius = 1.4 m
Height = 4.2 m
Volume of water filled in it = πr2h
= `22/7 xx 1.4 xx 1.4 xx 4.2 m^3`
= `181.104/7m^3`
= 25.872 m3 ...(i)
Diameter of pipe = 7 cm
Therefore, radius (r) = `7/2`
Let length of water in the pipe = h1
∴ Volume = πr2h1
= `22/7 xx 7/2 xx 7/2 xx h_1`
= `77/2 h_1 cm^3` ...(ii)
From (i) and (ii)
`77/2 h_1 cm^3 = 25.872 xx 100^3 cm^3`
`=> h_1 = (25.872 xx 100^3 xx 2)/77`
`=> h_1 = (25.872 xx 100^3 xx 2)/(77 xx 100)`
`=>` h1 = 0.672 × 1002m
`=>` h1 = 6720 m
Therefore, time taken at the speed of 4 m per second
= `6720/(4 xx 60)` minutes
= 28 minutes
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