Answer :

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]


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