Question

A spray irrigation system waters a section of a farmer’s field. If the water shoots a distance of 85 feet, what is the area that is watered as the sprinkler rotates through an angle of 60 degrees? Use 3.14 for pi . Round your answer to the nearest square foot, and enter the number only.

Answer 1

3,781

Explanation:

To solve this problem, we will find the area of the whole circle and use that to find teh area of the 60º section.

First, recognize the formula for the area of a circle:

A = 3.14
`r^(2)`

In this scenario, the radius (r) is 85 feet:

A = 3.14(85
`)^(2)`

A circle is 360º and we only require the area of 60º. 360º / 60º = 6 so we will divide by 6:

A =
`(3.14(85)^(2) )/(6)`

Finally, we will simplify and round:

A = 3,781