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Thread: Area of a sector

  1. September 20th 2009, 06:08 AM #1
    Chinnie15
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    Area of a sector

    The area of a circle is 72cm^2. Find the area of a sector of this circle that subtends a central angle of pi/6 rad.

    Thanks!
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  2. September 20th 2009, 06:53 AM #2
    e^(i*pi)
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    Quote Originally Posted by Chinnie15 View Post
    The area of a circle is 72cm^2. Find the area of a sector of this circle that subtends a central angle of pi/6 rad.

    Thanks!
    A_{sector} = \frac{1}{2}r^2 \theta

    A whole circle may be considered to be a sector:
    • A_{sector} = 72
    • \theta = 2\pi


    From this you can find r and then find the area of the sector.

    Spoiler:
    Rearranging the equation to find r and then plugging that expression in provides a way to find A in one step

    r = \sqrt{\frac{2A_{c}}{\theta_{c}}}

    A_s = A_c \, \frac{\theta_{s}}{\theta_c}

    Where:

    • A_s = Area of Sector
    • A_c = Area of Circle ( 72\, cm^2)
    • \theta_{c} = Angle of Circle ( 2\pi)
    • \theta_s = Angle subtended by sector ( \frac{\pi}{6}

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  3. September 20th 2009, 07:02 AM #3
    Grandad
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    Hello Chinnie15
    Quote Originally Posted by Chinnie15 View Post
    The area of a circle is 72cm^2. Find the area of a sector of this circle that subtends a central angle of pi/6 rad.

    Thanks!
    The whole circle ( 72\,cm^2) subtends an angle of 2\pi at the centre. The sector you want subtends an angle of \frac{\pi}{6} which is \frac{1}{12} of 2\pi. So its area is ...?

    Grandad
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  4. September 20th 2009, 04:57 PM #4
    Chinnie15
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    I figured it out, thanks!
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