A cone is formed by bending a sector of a circle with an angle of 210∘. Find the radius of the base of the cone if the diameter of the circle is 12 cm.
Worked solution (try it first)
The circle has diameter 12 cm, so its radius is 6 cm.
This radius becomes the slant height of the cone.
The arc of the sector becomes the circumference of the base: 360210×2π×6=2πr.
Divide both sides by 2π: r=6×360210=3.5 cm, option D.