Final answer:
To find the time it takes to half-fill a large hemispherical pan with water from a rectangular pipe, one must calculate the volume of half the pan and divide this by the flow rate of the water, which depends on the cross-sectional area of the pipe and the velocity of the water.
Step-by-step explanation:
The question asks how long it takes to half-fill a large hemispherical pan using water flowing from a rectangular pipe. To solve this, we need to calculate the volume that represents half of the hemispherical pan's capacity and then divide this by the flow rate of water from the pipe.
Calculating the Pan's Volume
The volume of a hemisphere is given by ½πr3, where r is the radius of the hemisphere. Here, the diameter is 3 meters (300 cm), so the radius is 1.5 meters (150 cm). Hence, the volume of the hemisphere is ½×π×1503. To find the volume of half of this, we simply divide this value by 2. The exact calculation is not included in the question, but this would be necessary to find the volume to be filled.
Calculating the Flow Rate from the Pipe
The flow rate from the pipe is given by the cross-sectional area of the pipe times the velocity of the water. The cross-sectional area of the rectangular pipe is 30 cm x 20 cm, and the velocity is 20 cm/second. Therefore, the flow rate is 30×20×20 cm3/s.
Finding the Time Required
We would divide the volume of water needed to fill half the pan by the flow rate of water coming from the pipe to get the time in seconds, then convert that to minutes for the final answer.
Without actual numbers, we cannot proceed to a definitive answer, but normally, through these calculations, we would identify the correct time required to half-fill the pan.