The height of the cone is 6 centimeters, and the generatrix is inclined to the base plane at an angle of 30

| June 17, 2021 | education

The height of the cone is 6 centimeters, and the generatrix is inclined to the base plane at an angle of 30 degrees. Find the cross-sectional area of a cone by a plane passing through two generatrices, the angle between which is 60 degrees.

In a right-angled triangle OCM, the OMC angle = 30, then the leg lying opposite this angle is equal to half the length of the hypotenuse CM, then CM = 2 * OC = 2 * 6 = 12 cm.

The section of the cone is a triangle CKM in which CK = CM as generators, and since, according to the condition, the angle CKM = 60, the triangle CKM is equilateral, CK = CM = KM = 12 cm.

Let’s define the cross-sectional area.

Ssection = a ^ 2 * √3 / 4, where a is the side of the triangle.

Ssection = 144 * √3 / 4 = 36 * √3 cm2.

Answer: The cross-sectional area is 36 * √3 cm2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.