Football Field Problems

Problem three consists of a football field that needs a new irrigation system. The best route for the water pipes, location of the sprinklers, what part of the field each sprinkler waters, and how much of the field each sprinkler waters had to be determined. While figuring this out, the whole football field has to be watered without being over watered. The sprinkler placed in the corners will cover ¼ of a circle and it will spray at a 90 degree angle. The sprinklers that cover the border will water half a circle and it has to spray at a 180 degree angle. Lastly, the sprinklers within the field will cover a full circle and it will spray at a 360 degree angle. . To determine the number of sprinklers, the number of sprinklers at the width and the length were multiplied so 5 was multiplied by 10 which equals 50 sprinklers in total. The sprinklers have been set up 40 ft. from each other around the football field. The pipes were placed all throughout the football field. For example, the pipes being used in this irrigation system were placed in 5 rows across the field and they were connected at the ends with two other pipes.
The sprinklers at the corner of the football field cover 1,256 ft to determine that, the formula for the area of a sector was used which is A= 0/360 x 3.14 x R x R .
Next, the sprinklers surrounding the field cover 2,512 ft. to solve that, the formula used was the for the area of a sector. Last, the sprinklers in the football field covers 5,024 feet and to figure that out, the formula for an area of a circle was used. Each Orbit 4-inch Gear Drive Pop Up Sprinkler costs 11 dollars and the total amount of sprinklers are 50 so 11 was multiplied by 11 which came to a total of 550 dollars. The total feet for piping was 1960. To solve the total amount for the piping, 1960 was multiplied by .75 which came to the total of 1,470
dollars.
In conclusion, the best route for the water pipes was the pipes being placed across the football field,also the sprinklers were placed 40 feet apart, as stated the sprinklers will either water a quarter, half, or a full circle and the quarter circle will water 1,256 feet, the half circle will water 2,512 feet, lastly the full circle will water 5,024 feet. Adding up the total for the sprinklers which was 550 and adding up the total for the piping which was 1960, the total cost for everything came to be 2,020 dollars.