Ashley has a sprinkler that has several varieties of coverage. The quarter circle sprinkler head sprays water a distance of up to 20 feet from the lead. What area will be covered by the spray of the quartercircle sprinkler head to the nearest square foot?

The area the quarter-circle sprinkler sprays with water is 314 square feet.

Step-by-step explanation:

Step 1; It is given that the quarter-circle sprinkler can reach a distance of 20 feet, the radius of the circle will be equal to 20 feet.

Step 2; The area of any given circle is π times the square of the radius. The radius of this circle is equal to 20 feet.

Area of the circle = π * r² = 3.1415 * 20 * 20 = 1,256.6370 square feet.

Step 3; 1,256.6370 square feet is the area of a full circle with a radius of 20 feet. The sprinkler only covers a quarter of the circle so we divide the area by 4 to convert it into a quarter-circle.

Area of the quarter circle = 1,256.6370 square feet / 4 = 314.1592 square feet.

So the quarter sprinkler covers an area of 314.1592 square feet.