A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled(in minutes)?
100
Let cylindrical tank be filled in x hours
Diameter of pipe = d =20 cm
⇒ Radius of pipe = r=202=10cm=0.1m
Speed of water flowing through pipe = 3 km/h = 3000 m/h
Volume of water flowing through pipe in 1 hour = π.r2.h=π×0.1×0.1×3000=30πm3
Volume of water flowing through pipe in x hours =30x.πm3
Diameter of cylindrical tank = d1=10m
Radius of cylindrical tank = r1=102=5m
Height of cylindrical tank = h1=2m
Volume of cylindrical tank = π.(r1)2.h1=π×5×5×2=50πm3
According to given condition we have:
Volume of water flowing through pipe in x hours = Volume of cylindrical tank
⇒ 30x.π =50π
x=5030=53 hours=100 minutes