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Given: R=2m
KL = LM = KM
Find: V and
Surface Area of the cone

 

 Apr 26, 2020
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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  

 Apr 26, 2020

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