Water flows at the rate of 10m min-1 through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
Let the time taken by pipe to fill vessel is t minutes
As water flows 10 m in 1 minute, it will flow 10t meters in t minutes.
Also,
Volume of conical vessel = Volume of water that passes through pipe in t minutes
Now, For conical pope
Base Diameter = 40 cm
Base radius, r = 20 cm
[as radius = diameter/2]
Height, h = 24 cm
We know that,
Where, r is base radius and h is the height of the cone.
Volume of conical vessel
For cylindrical pipe
Base diameter = 5 mm = 0.5 cm
[As 1 cm = 10 mm]
Base radius, r = 0.25 cm
[as radius = diameter/2]
Height, h = 10t m = 1000t cm
[∵ 1 m = 100cm]
[As water covers 10t m distance in pipe]
As we know,
Volume of a cylinder = πr2h
Where r is base radius and h is the height of cylinder
Volume of water passed in pipe = π(0.25)2(1000t) = 62.5tπ cm3
So, we have
62.5tπ = 3200
62.5t = 3200
t = 51.2 minutes
t = 51 minutes 12 seconds
[ as 0.2 minutes = 0.2(60) seconds = 12 seconds]