A sector of a circle of radius 8cm is bent to form a cone. Find the radius of the cone and it's vertical angle if the angle substended at the centre by the sector is 280°

Answer 1

If you make a sketch you will see that the arc length of the
sector becomes the circumference of the the base of the cone
For the sector, arc = rØ , where Ø must be in radians.
280° = 280π/180 rads = 14π/9 rad

Then for the cone's circular base,
2πr = 14π/9
r = 7/9 cm

Answer 2

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