Final answer:
The area that is sprayed with water by the sprinkler rotating 160° with a radius of 7 ft is (196/9) × π square feet, calculated using the formula for the area of a sector of a circle.
Step-by-step explanation:
To find the area that is sprayed with water by the sprinkler, we need to calculate the area of a sector of a circle. The formula for the area of a sector with a central angle in degrees is given by:
Area of Sector = (θ/360) × π × r^2
Where θ is the central angle in degrees and r is the radius of the circle. Given that the sprinkler rotates 160° and has a radius of 7 ft, we can apply these values to the formula:
Area of Sector = (160/360) × π × (7 ft)^2
Area of Sector = (4/9) × π × 49 ft^2
Area of Sector = (196/9) × π ft^2
The exact area that is sprayed with water is (196/9) × π square feet.