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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?

 Aug 10, 2021
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The cone will now hav a circumference of    pi * 30  -   pi*30 (144/360) = 56.549 units

    this will be a diameter of     56.549/pi   = 18        radius of  9  units

 

the side length will still be 15  units

 

sin of 1/2 of the vertex =  opp / hyp = 9/15   

   arcsin (9/15 ) = 36.87 degrees                              2 x 36.87 = 73.74 degrees            

 Aug 10, 2021

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