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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