The volume of the conical vessel is calculated as one-third times pi times the radius squared times the height, which equals one-third times pi times 20 squared times 24, or 3200 pi cubic centimeters. The cylindrical pipe has a radius of 0.25 centimeters, so its cross-sectional area is pi times 0.25 squared, or 0.0625 pi square centimeters. Water flows at 10 meters per minute, which is 1000 centimeters per minute, so the pipe fills 1000 times 0.0625 pi, or 62.5 pi cubic centimeters per minute. Dividing the vessel volume by the flow rate gives 3200 pi divided by 62.5 pi, which equals 51.2 minutes; this converts to 51 minutes and 12 seconds.