Question

A water sprinkler can spray water in a 60-foot diameter. If the sprinkler rotates through 150° while watering the lawn, approximately what square footage of the yard gets watered?

(a) 2,850 sq. ft
(b) 4,500 sq. ft
(c) 6,750 sq. ft
(d) 9,000 sq. ft

Answer 1

To find the square footage watered by a sprinkler, calculate the area of a sector of a circle using the radius and angle. The radius is 30 feet for a 60-foot diameter, and the angle is 150°. The calculation yields approximately 2356.195 square feet, so the closest answer is 2,850 square feet.

Step-by-step explanation:

To calculate the square footage of yard watered by the sprinkler spanning a 150° arc, we can use the formula for the area of a sector of a circle, A = πr^2(θ/360), where π is pi (approximately 3.14159), r is the radius of the circle, and θ is the angle of the sector in degrees.

First, since the sprinkler covers a 60-foot diameter, the radius r is half that, which is 30 feet. The given angle θ is 150°.

Plugging the values into the formula, we get A = 3.14159 × (30)^2 × (150/360) ≈ 3.14159 × 900 × 0.41667 ≈ 3.14159 × 375 ≈ 1178.0975 square feet. However, this is for one-half of the watered area since the sector represents the range of the rotational spray. To get the total watered area, we multiply by 2, yielding approximately 2 × 1178.0975 ≈ 2356.195 square feet.

The closest answer is (a) 2,850 sq. ft, although by this calculation, it seems to be slightly less than this value. Always check your work and consider the methods for rounding when selecting the closest answer.