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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?

Respuesta :

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.

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