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# 3d geometry

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A sector of 144 degrees is removed from a circle of radius 15, and the remaining portion is folded into a cone. What is the angle at the vertex of the cone?

Oct 2, 2021

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A sector of 144 degrees is removed from a circle of radius 15, and the remaining portion is folded into a cone. What is the angle at the vertex of the cone?

The original radius will become the slant height, so the slant height will be 15units

360-144=216 degrees

$$New\; Circumference=\frac{216}{360}*2\pi r\\ New\; Circumference=\frac{216}{360}*2\pi *15\\ New \;Circumference\approx18\pi\;\;units$$

$$C=2\pi r\\ 18\pi=2\pi r\\ r=9\;\;units$$