A cardboard imn the shape of a sector of radius 12cm is folded to form a right circular cone. If the arc of the sector subtends angle 90 degree at the centre, calculate the radius of the cone.
the arc length is 90/360 = 1/4 of a circle, or 1/2 π r = 6π
That is the whole circumference of the cone, so its radius is 6π/2π = 3 cm
it's no accident that that is 1/4 the radius of the sector.