A circle has a sector with area 33 pi and central angle of 11/6 pi radians. What is the area of the circle?

Question

A circle has a sector with area 33 pi and central angle of 11/6 pi radians. What is the area of the circle?

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Maria 2 months 2021-10-03T18:01:40+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-03T18:02:51+00:00

    Answer:

    The area of the circle is 36\pi\ units^{2}

    Step-by-step explanation:

    we know that

    The area of a circle subtends a central angle of 2\pi radians

    so

    By proportion find the area of the circle

    \frac{33\pi }{(11\pi /6)}=\frac{x}{2\pi}\\ \\ x=2\pi*( 33*6)/11\\ \\x=36\pi\ units^{2}

    0
    2021-10-03T18:03:38+00:00

    Answer:

    Step-by-step explanation:

    Area of the sector =

    [pi*r^2*11*pi/6]/360=pi^2*r^2*11/6*360=pi*r^2*11*180/2160=33 pi

    r^2=71280/11*pi=6480/pi=6480/180=36

    Area of the circle=pi*r^2=36 pi

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