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?
+118608 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.
