Question

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? 

Answer 1

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.