Since the triangle is an equilateral triangle, the incenter will be the center of the sphere (label this point C).
The incenter is two-thirds of the distance from a vertex to the midpoint of the opposite side; therefore LO = (3/2)·LC.
Since LC = 2m; LO = 3m
Triangle LOK is a 30-60-90 right triangle, making KO = sqrt(3)·m and LK = 2·sqrt(3)·m.
Formula for the volume of a cone: V = (1/3)·pi·r2·h = (1/3)·pi·[sqrt(3)·m]2·3m
Formula for the surface area of a cone: SA = pi·r·L + 2·pi·r2 = pi·sqrt(3)·m·2·sqrt(3)·m + 2·pi·[sqrt(3)·m]2