#1**+1 **

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·r^{2}·h = (1/3)·pi·[sqrt(3)·m]^{2}·3m

Formula for the surface area of a cone: SA = pi·r·L + 2·pi·r^{2} = pi·sqrt(3)·m·2·sqrt(3)·m + 2·pi·[sqrt(3)·m]^{2}

geno3141 Apr 26, 2020