Anonymous asked in Science & MathematicsMathematics · 1 decade ago

Area of a sector?

How do I find the area of a sector when given angle of 30 degrees and length of arc as 6 pi?

2 Answers

  • 1 decade ago
    Favorite Answer

    30/360 = 1/12 of a complete circle.

    If the arc is 6pi, the circumference is 12 * 6 pi = 72 pi.

    divide by pi to get the diameter: 72.

    The radius is half that, or 36.

    The area of the complete circle is pi * 36^2, or 1296 pi. The area of the sector is 1/12th of that.

    1296pi / 12 = 108 pi

    But you'll need to tack on the units to that answer.

    108 pi square meters?

    108 pi square inches?

  • 1 decade ago

    If you have the angle, and the length of the arc, you can work out the radius (hint, convert the angle into radians, then see )

    As you then have the radius, and the fraction of a circle represented by 30degrees, you can then work out the area of the sector

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