Question

Water flows at the rate of 15 m per minute through a cylindrical pipe, having the diameter 20 mm. How much time will it take to fill a conical vessel of base diameter 40 cm and depth 45 cm?

Answer 1

Diameter of a pipe = 20 mm ….(given)

Radius of the pipe = `20/2` mm = 10 mm = 1 cm

Speed of water = 15 m/min= 1500 cm/min
Volume of cylinder = πr² h
Volume of water that flows in pipe in 1 minute

= `22/7xx1^2xx1500`

= `33000/7"cm"^3`

Radius of conical vessel = `40/2` = 20 cm

Depth 45 cm ... Given

Capacity of the conical vessel  

`=1/3pir^2h`

=`1/3xx22/7xx20xx20xx45`

`=396000/21"cm"^3`

Time required to fill the vessel                                    `="Capacity of the vessel"/ "Volume of water flowing per minute"`

`=(396000/21)/(33000/7)`

`=396/99`

= 4 minutes

Thus, the time required to fill the conical vessel is 4 minutes.