Cone height 3√3. Its generatrix is inclined to the plane of the base at an angle of 60.

| February 12, 2021 | education

Cone height 3√3. Its generatrix is inclined to the plane of the base at an angle of 60. Around the cone, a sphere whose radius is less than the height of the cone is described. Find the surface area of the ball.

Since the generatrix of the cone is inclined to the base plane at an angle of 60, the axial section of the cone is an equilateral triangle ABC, since AC = BC as generators, and one of the angles is 60, then AB = AB = BC.

In an equilateral triangle, its medians intersect at point O, the center of the circumscribed circle and are divided at point O in the ratio of 2/1, then OС = 2 * OС / 3 = 2 * 3 * √3 / 3 cm.

R = OС = 2 * √3 cm.

Let us determine the surface area of the ball. Sball = 4 * π * R2 = 4 * π * 4 * 3 = 48 * π cm2.

Answer: The surface area of the ball is 48 * π cm2.



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