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Sagot :
The total area covered by the yard by the 3 sprinkler heads such that each covers a circular area with no overlap is 5892.857 ft².
What is the area of a circle?
The area of a circle is the area covered by the circle with radius r. It is given by the formula,
[tex]\text{Area of circle} = \pi r^2[/tex]
As it is given that the area covered by a single sprinkler system is of the radius of 25 feet, therefore, the area covered by a singular sprinkler system can be written as,
Area of sprinkler = Area of a circle with radius 25 feet
[tex]\begin{aligned}\text{Area of sprinkler}&= \pi r^2\\&=\pi (25^2)\\&= 1964.2857 \approx 1964.286\rm\ ft^2\end{aligned}[/tex]
Now, as we know that the yard has three such sprinkler systems, therefore, the area covered by the sprinkler will be thrice the area covered by a single sprinkler,
The total area covered by the sprinkler = 3 x Area of sprinkler
= 3 x 1964.286
= 5892.857
Thus, the total area covered by the yard by the 3 sprinkler heads such that each covers a circular area with no overlap is 5892.857 ft².
Learn more about the Area of Circle:
https://brainly.com/question/1238286
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