A plane is drawn through the apex of the cone that intersects the base along a chord that contracts an

| May 7, 2021 | education

A plane is drawn through the apex of the cone that intersects the base along a chord that contracts an arc of 90 degrees. Find the S side of the surface of the cone if the generatrix is 10 and the angle in the section at the vertex is 60.

In a triangle CA = CB = 10 cm, since they are generators of the cone. The angle ACB, by condition, is 60, then the angles CAB and CBA are equal to 60, and the triangle ABC is equilateral.

The degree measure of the arc AB is equal to 90, then the central angle AOB is also equal to 90, and the triangle AOB is rectangular and isosceles. ОА = ОВ = R.

Then, by the Pythagorean theorem, AB ^ 2 = R ^ 2 + R ^ 2 = 2 * R ^ 2

R ^ 2 = AB / 2 = 100/2 = 50.

R = √50 = 5 * √2 cm.

Let us determine the area of the lateral surface.

Sside = n * R * AC = n * 5 * √2 * 10 = n * 50 * √2 cm2.



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