A sprinkler covers an area of 405 ft2. It rotates a total of 155°. How far does the water spray from the sprinkler head?
Question
A sprinkler covers an area of 405 ft2. It rotates a total of 155°. How far does the water spray from the sprinkler head?
Solution
To solve this problem, we need to understand that the area covered by the sprinkler is a sector of a circle. The formula for the area of a sector is (θ/360) * π * r², where θ is the angle the sector subtends at the center of the circle, and r is the radius of the circle.
Here, the area A is given as 405 ft² and the angle θ is 155°. We need to find the radius r, which represents the distance the water sprays from the sprinkler head.
Rearranging the formula for r, we get r = sqrt(A / [(θ/360) * π]).
Substituting the given values, we get r = sqrt(405 / [(155/360) * π]).
Now, calculate the value inside the square root: 405 / [(155/360) * π] ≈ 405 / 1.36 ≈ 297.79.
Finally, take the square root of this result to find r: r = sqrt(297.79) ≈ 17.26 ft.
So, the water sprays approximately 17.26 feet from the sprinkler head.
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