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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

    

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

 

Now find the cone radius

\(C=2\pi r\\ 18\pi=2\pi r\\ r=9\;\;units\)

 

Now draw the pic and use trigonometry to find any angle that you please. 

 Oct 3, 2021

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