Let the time taken by pipe to fill vessel = t minutes
Since water flows 10 m in 1 minute, it will flow 10t meters in t minutes.
According to the question,
Volume of conical vessel = Volume of water that passes through pipe in t minutes
Consider conical pope
Base Diameter = 40 cm
Base radius, r = 20 cm
Height, h = 24 cm
We know that the volume of cone = 1/3πr2h
Volume of conical vessel = 1/3π(20)2(24) = 3200 π cm3
Consider cylindrical pipe
Base diameter = 5 mm = 0.5 cm
Base radius, r = 0.25 cm
Water covers 10t m distance in pipe,
Hence, we get,
Height, h = 10t m = 1000t cm
We also know that,
Volume of a cylinder = πr2h
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
We know that,
0.2 minutes = 0.2(60) seconds = 12 seconds
Therefore, t = 51 minutes 12 seconds