Question

an individual head of a sprinkler system covers a circular area of grass with a radius of 25 feet. the yard has 3 sprinkler heads that each cover a circular area with no overlap. what is the approximate total area that will be watered?
○ 1963.5 ft
○ 1963.5 ft²
○ 5890.5 ft
○ 5890.5 ft²

Explanation:

Step1: Recall the formula for the area of a circle

The area of a circle is given by the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle.

Step2: Calculate the area of one sprinkler head's coverage

Given that the radius \( r = 25 \) feet, we substitute this into the formula. Using \( \pi \approx 3.1416 \), we have:
\( A_{1} = \pi \times (25)^2 = 3.1416\times625 = 1963.5 \) square feet (this is the area for one sprinkler head).

Step3: Calculate the total area for 3 sprinkler heads

Since there are 3 sprinkler heads with no overlap, we multiply the area of one sprinkler head by 3. So, \( A_{total}=3\times A_{1} = 3\times1963.5 = 5890.5 \) square feet.

Answer:

\( 5890.5\ \text{ft}^2 \) (corresponding to the option "5890.5 ft²")