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Math Help - how to calculate the area and arc length of a given sector of a circle?

  1. #1
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    how to calculate the area and arc length of a given sector of a circle?

    I need to calculate the area and arc length of a major sector of a 60mm diameter circle. the sector is 252 degrees. how do i do this?

    Thanks in advance.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Arc length = r\theta

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

    Otherwise,

    Arc\ length = 2\pi r \times \dfrac{\theta}{360^o}

    for theta in degrees.

    Similarly,

    Area\ of\ segment = \dfrac12 r^2 \theta

    for theta in radians and

    Area\ of\ segment = \pi r^2 \times \dfrac{\theta}{360^o}

    for theta in degrees.
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  3. #3
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    That is brilliant thank you very much. another question, what formula do i use? how do i decide between radians and degrees?
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  4. #4
    MHF Contributor Unknown008's Avatar
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    Well, were you taught the formulae I gave you where theta is in radians?

    Using those formulae is faster, but since you were given the angle in degrees, you better use that.

    Also, you see how I got those formulae where theta is in degrees?

    For the arc length, it is the circumference of a circle, multiplied by the angle divided by 360 degrees.
    For the area, it is the area of a circle, multiplied by the angle divided by 360 degrees.
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  5. #5
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    thats brilliant, thank you for your help.
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