Question

A sprinkler rotates through an angle of 115° spraying water outward for a distance of 12 ft. find the exact area watered, then round the result to the nearest tenth of a square foot.

Answer 1

The sprinkler rotates through an angle of 115° and sprinkles water outward for a distance of 12 ft.
Therefore the radius of the circular section is 12 ft as shown in the diagram below.

The total circle occupies 360°. Therefore the area watered is
A = (115/360)*π*(12 ft)²
= 144.513 ft²

Answer: 144.5 ft (nearest tenth)