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A circular piece of wire has a radius of 12 cm. This is cut then bent to form an arc of a circle whose radius is 60 cm. Find the angle subtended at the centre by this arc. Give your answer to the nearest degree.

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Thank you so much!

  • Math -

    the circumference of the original circle becomes the arc length of the sector.
    circumf. of circle = 2πr = 24π

    arc = rØ, were Ø is the central angle in radians and r is the radius
    so if r = 60
    60Ø = 24π
    Ø = 24π/60 radians = 2π/5 radians

    I know π/5 radians = 36° , so
    2π/5 radians = 72°

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