Fan-shaped problems in junior high school mathematics

Cut the largest circle in the fan-shaped OAC as the bottom surface, and let the radius of this circle be r, then r+2r=9 (this circle is equal to the big one.

And the radii of the two sides are tangent), r=3. The circumference of this circle =6π, and the arc length of the sector OBC =9π*(2/3) (because the angle BOC= 120 and the angle AOC=60)=6π, so it is ok.

The circumference of the cone bottom = the arc length of the sector OBC =6π, the radius of the cone bottom =3, the generatrix of the cone =9, the radius and height, and the generatrix forms a right triangle. According to Pythagorean theorem, it is concluded that = root sign (9? -3? ) =6 times the root number 2.