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 ft1963.5 ft²5890.5 ft5890.5 ft²

Explanation:

Step1: Find area of one sprinkler

The area of a circle is $A = \pi r^2$. Substitute $r=25$ ft:
$A_1 = \pi (25)^2 = 625\pi$

Step2: Calculate total area for 3 sprinklers

Multiply single area by 3:
$A_{total} = 3 \times 625\pi = 1875\pi$

Step3: Approximate with $\pi\approx3.1416$

$A_{total} \approx 1875 \times 3.1416 = 5890.5$
Area uses square units, so units are $\text{ft}^2$.

Answer:

5890.5 ft²