Mathematics
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.
Mensuration
ICSE
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Answer
Given,
Diameter of cylindrical tank = 2.8 m
So, its radius (R) = = 1.4 m
Height (H) = 4.2 m
Volume of water filled in it = πr2h
= x 1.4 x 1.4 x 4.2
= 25.872 m3
= 25.872 × (100)3 cm3
Given,
Diameter of the pipe = 7 cm
Radius (r) = = 3.5 cm
Area of cross section of pipe = πr2
=
= 22 × 0.5 × 3.5
= 38.5 cm2.
Volume of water discharged per second = 38.5 cm2 × 4 m s-1
= 38.5 × 400 cm s-1
Let the pipe fill the tank in n seconds.
∴ n × Volume of water discharged per second = Volume of tank
Hence, it takes 28 minutes to fill the tank.
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