Water flows at the rate of `10` meter per minute through a cylindrical pipe having diameter as `5` `mm`. How much time will it take to fill a conical vessel whose diameter of base is `40` `cm` and depth `24` `cm`?

Explanation

Given, speed of water flow `=10 m min ^(-1) = 1000 cm// min`
and diameter of the pipe ` = 5 mm = (5)/(10 ) cm`
`therefore ` Radius of the pipe `= (5)/(10 xx 2) = 0.25 cm`
`therefore ` Area of the face of pipe `= pir^(2) = (22)/(7) xx (0.25)^(2) = 0. 1964 cm^(3)`
Also , given diameter of the conical vessel = 40 cm
Radius of the conical vessel `= (40)/(2) = 20 cm `
and depth of the conical vessel = 24 cm
and depth of the conical vessel `= (1)/(3) pir^(2)h = (1)/(3) xx (22)/(7) xx (20)^(2) xx 24`
`= (211200)/(21) = 10057.14 cm^(3)`
`therefore " ""Required time"= ("Volume of the conical vessel")/("Area of the face of pipe"xx"Speed of water")`
`= (10057.14)/(0.1964 xx 10xx 100)`
`= 51.20 min = 51 min (20)/(100) xx 60 s = 51 min 12 s`