A circle has a sector with area 1/2 pi and central angle of 1/9 pi radians. What is the area of the circle

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A circle has a sector with area 1/2 pi and central angle of 1/9 pi radians. What is the area of the circle

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Madelyn 2 weeks 2021-11-20T14:07:20+00:00 1 Answer 0 views 0

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    2021-11-20T14:08:42+00:00

    Answer:

    9\pi sq. units.

    Step-by-step explanation:

    It is given that a circle has a sector with area \frac{1}{2}\pi and central angle of \frac{1}{9}\pi radians.  

    We know that, the area of sector is

    A=\dfrac{1}{2}r^2\theta

    where, r is radius and \theta is central angle in radian.

    Substitute the values of A and \theta.

    \dfrac{1}{2}\pi=\dfrac{1}{2}r^2(\dfrac{1}{9}\pi)

    1=r^2(\dfrac{1}{9})

    9=r^2

    3=r

    The radius of the circle is 3 units.

    So, the area of circle is

    A=\pi r^2

    A=\pi (3)^2

    A=9\pi

    Therefore, the area of circle is 9\pi sq. units.

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