The angle at the apex of the axial section of a cone with a height of 1 m is equal to 1200. What is the cross-sectional area

| February 12, 2021 | education

The angle at the apex of the axial section of a cone with a height of 1 m is equal to 1200. What is the cross-sectional area of a cone drawn through two generatrices, the angle between which is 600.

The axial section of the cone, there is an isosceles triangle ABC, which OB has the cone height and height, the bisector and median of the ABC triangle.

Then the ВOС triangle is rectangular, in which the OBC angle = 120/2 = 60, the OCВ angle = (90 – 60) = 30.

The OB leg lies against the angle 30, then BC = 2 * OB = 2 * 1 = 2 m.

The KВН triangle is a section of a cone with an apex angle B = 60, and its sides are equal to the generatrix of the cone, BM = BH = BC = 2 m.

Then Svnk = ВK * ВН * SinKВН / 2 = 2 * 2 * Sin60 / 2 = 4 * √3 / 4 = √3 cm2.

Answer: The cross-sectional area is √3 cm2.



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