A 210 degrees of a sector of radius 5cm is bent on form cone. For the fone formed find a.the base radius of the cone b.the vertical angle of the cone c.the curved surface area of the cone.

Answer 1

If you make a sketch, you will see that the arc length subtended by the 210° sector angle will become the circumference of the base of the cone.
arc/(10π) = 210/360
arc = 10π(1/3) = 10π/3

let the radius of the base be r
2πr = 10π/3
r = 10π/(6π) = 5/3
the slant height of the cone = 5
tanØ = 5/(5/3) = 1/3, where Ø is the base angle

I will let you find the angle, as well as the surface area of the cone.
for b) how does the curved surface of the cone related to the area of the sector??