Sprinkler heads come in all different sizes depending on the angle of rotation desired. If a sprinkler head rotates 90 ° and has enough pressure to keep a constant 25-foot spray, what is the area of the sector of the lawn that gets watered? Round to the nearest square foot.

491 ft²

Step-by-step explanation:

We know the area of a sector, A = Ф/360° × πr² where Ф = angle subtended by sector = angle of rotation of sprinkler = 90° and r = radius of sector = length of spray = 25 feet.

Substituting the values of the variables into the equation, we have

A = Ф/360° × πr²

A = 90°/360° × π(25 ft)²

A = 1/4 × 625π ft²

A = 1/4 × 1963.5 ft²

A = 490.9 ft²

A ≅ 491 ft² to the nearest square foot