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math

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the arc length and central angle of a circle are 10cm and 80degrees respectivly. what is the length of the radius?

  • math - ,

    Circumference of a circle

    C = 2 r pi


    the arc length

    L = 2 r pi * theta / 360 °

    = r * pi * theta / 180°


    10 = r pi * 80 / 180 Multiply both sides by 180

    10 * 180 = r * pi * 80

    1800 = r * pi * 80 Divide both sides by 80 pi


    1800 / 80 pi = r

    r = 1800 / 80 pi

    r = 40 * 45 / ( 40 * 2 * pi )

    r = 45 / 2 pi

    r = 45 / ( 2 * 3.14159 )

    r = 45 / 6.28318

    r = 7.162 cm

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