Water is flowing at the rate of 3km/hr through a circular pipe of 20cm internal diameter into a circular cistern of diameter 10m and depth 2m. In how much time will the cistern be filled?

Explanation

Internal diameter ofpipe =20
`therefore` Internal radius of pipe =10 cm =`(1)/(10)m`
Rate of flow of water =`3m/h`
Rate of flow of water =`(3xx1000)/(60xx60)m/sec`
Diameter of cistern =10m
Radius of cistern=5 m
Height of cistern =2m
Water discharge by pipe in 1 sec
`=pixxr^(2)xx`flow fo water
`=pixx((1)/(10))^(2)xx(3xx1000)/(60xx60)m^(3)//sec`
Volume of cistern =`pixx5^(2)xx2m^(3)`
Time taken to fill the cistern =`("volume of cistern")/("volume of water discharge in 1 sec")`
`=(pixx25xx2)/(pixx(1)/(100)xx(3xx10000)/(60xx60))sec=(25xx2xx100xx60xx60)/(3xx1000)`sec
`=(5xx60xx60)/(3)sec=(5xx60xx60)/(3xx60xx60)"hours" =(5)/(3)` hours