Diameter of the pipe = 5 mm = 5/10cm = 1/2cm
∴ Radius of the pipe = 1/2 x 1/2cm = 1/4cm.
In 1minute, the length of the water column in the cylindrical pipe = 10m = 1000cm.
∴ Volume of water that flows out of the pipe in 1minute = π x 1/4 x 1/4 x 1000cm3.
Also, volume of the cone = 1/3 x π x 20 x 20 x 24cm3.
Hence, the time needed to fill up this conical vessel
= 256/5minutes = 51.2minutes.
Hence, the required time is 51.2minutes.