The cone is inscribed in a regular quadrangular pyramid, in which the height is 6√3 cm, the side of the base

| May 3, 2021 | education

The cone is inscribed in a regular quadrangular pyramid, in which the height is 6√3 cm, the side of the base is 12 cm. Find the area of the lateral surface of the cone.

Since the pyramid is correct, at its base lies a square ABCD with a side of 12 cm.

Then the radius of the circle at the base of the inscribed cone is equal to half the length of the side of the square. R = OH = AD / 2 = 12/2 = 4 cm.

The lateral edges of the pyramid are isosceles triangles, then the height of the PH of the PCD triangle is its median, as well as the generator of the inscribed cone.

The RON triangle is rectangular, in which, according to the Pythagorean theorem, we determine the length of the RN hypotenuse. PH ^ 2 = OP ^ 2 + OH ^ 2 = 108 + 36 = 144.

PH = L = 12 cm.

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

Side = π * R * L = π * 6 * 12 = 72 * π cm2.

Answer: The area of ​​the lateral surface of the cone is 72 * π cm2.



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