# The axial section of the cone is an isosceles right-angled triangle with a hypotenuse equal to C.

October 5, 2021 | education

| **The axial section of the cone is an isosceles right-angled triangle with a hypotenuse equal to C. Find the area of the lateral surface of the cone.**

The hypotenuse of the triangle ABC is the diameter of the circle at the base of the cone, then the radius of the circle is: R = AO = AC / 2 = C / 2 cm.

The ABC triangle is rectangular and isosceles, then, according to the Pythagorean theorem, AC ^ 2 = 2 * AB ^ 2.

AB ^ 2 = AC ^ 2/2.

AB = AC / √2 = C / √2 = C * √2 / 2 cm.

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

Side = π * AO * AB = π * (C / 2) * (C * √2 / 2) = π * C ^ 2 * √2 / 4 cm2.

Answer: The lateral surface area is π * C ^ 2 * √2 / 4 cm2.

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