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Math Help - radians

  1. #1
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    Exclamation radians

    A sector of a circle has a radius of 10 cm and contains an angle of 150 degress. A hollow right circular cone is formed by bending the sector round until the bounding radii meet. Find the radius of the base of the cone and its semi-vertical angle.
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  2. #2
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    arc length of sector = circumference of circular base

    10\left(150 \cdot \frac{\pi}{180}\right) = 2\pi r

    solve for r , the radius of the cone's base.


    cone's semi-vertex angle = \sin^{-1}\left(\frac{r}{10}\right)
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