Through the apex of the cone, a cross-section is drawn that intersects the base along a chord

| February 8, 2021 | education

Through the apex of the cone, a cross-section is drawn that intersects the base along a chord equal to 4 dm and cutting off the arc of 90 degrees. Find the lateral surface area of the cone if the apex angle is 60 degrees.

The section of the cone is an equilateral triangle of СDK, since KС = KD as generators of the cone, and one of its acute angles is 600, then KС = KD = SD = 4 dm.

According to the condition, the degree measure of the СDВ arc is equal to 900, then the central angle of the SOD based on it is also 900, and then the СOD triangle is rectangular and isosceles, OC = OD = R.

From a right-angled triangle СOD, according to the Pythagorean theorem, СD^2 = R^2 + R^2 = 2 * R^2.

R:2 = CD^2 / 2.

R = 4 / √2 cm.

Let us determine the area of ​​the lateral surface of the cone.

Side = n * R * KС = π * (4 / √2) * 4 = π * 16 / √2 = π * 8 * √2 cm2.

Answer: The area of ​​the lateral surface of the cone is π * 8 * √2 cm2.



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