The irrigation system for a farm sprays water in circular patterns. Each sprinkler is connected to a pipe in the center of a circle and rotates around that pipe. The largest sprinkler sprays water 20 feet. What is the circumference of the circle irrigated by this sprinkler?
Here the irrigation sprinkler is pivoted at an angle θ = 40 ∘ = 40 π 180 rad. It waters a circular sector of area A = 2060 f t 2 . If the length of the sprinkler be L ft. It will be radius of the circular sector watered. Hence 1 2 × θ in radian × L 2 = A ⇒ L = √ 2 A θ = √ 2 ⋅ 2060 ⋅ 180 40 π ≈ 76.8 ft
