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Math Help - Designing a Water Sprinkler

  1. #1
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    Designing a Water Sprinkler

    An engineer is asked to design a water sprinkler that will cover a field of 100 square yards that is in the shape of a sector of a circle of radius 50 yards. Through what angle should the sprinkler rotate?
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  2. #2
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    Hello, magentarita!

    An engineer is asked to design a water sprinkler that will cover a field
    of 100 square yards that is in the shape of a sector of a circle of radius 50 yards.
    Through what angle should the sprinkler rotate?

    We are expected to know the area formula for a sector of a circle: . A \:=\:\tfrac{1}{2}r^2\theta .[1]

    . . where r is the radius and \theta is the central angle in radians.


    We know: . A = 100,\;r = 50

    Substitute into [1]: . 100 \:=\:\tfrac{1}{2}(50^2)\theta


    Therefore: . \theta \;=\;0.08\text{ radians} \;\approx\;4.58^o

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  3. #3
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    wow....

    Quote Originally Posted by Soroban View Post
    Hello, magentarita!


    We are expected to know the area formula for a sector of a circle: . A \:=\:\tfrac{1}{2}r^2\theta .[1]

    . . where r is the radius and \theta is the central angle in radians.


    We know: . A = 100,\;r = 50

    Substitute into [1]: . 100 \:=\:\tfrac{1}{2}(50^2)\theta


    Therefore: . \theta \;=\;0.08\text{ radians} \;\approx\;4.58^o
    I had no idea it was that simple.
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