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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- Dec 30th 2008, 06:15 AMmath123456radians
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.

- Dec 30th 2008, 06:27 AMskeeter
arc length of sector = circumference of circular base

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

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

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