Question

ДОРОГАЯ задача на тему "Конус" 1. Найдите площадь полной поверхности конуса, если периметр его осевого сечения равен 16 см, а угол развёртки боковой поверхности 120 градусов. Т.к. задача сложные, то и цена соответствующая. За самый качественный ответ поставлю Лучший!

Answer 1

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Answer 2

Task: Find the total surface area of a cone

To find the total surface area of a cone, we need to use the formula that involves the slant height and the radius of the base. The given information includes the perimeter of the base and the angle of the lateral surface, which can be used to calculate the slant height and the radius.

Given Information:

- Perimeter of the base (P) = 16 cm - Angle of the lateral surface (θ) = 120 degrees

Calculating the Slant Height (l):

The slant height (l) can be calculated using the formula: l = P / (2 * π)

Substitute the given perimeter (P) into the formula: l = 16 / (2 * π)

Calculating the Radius (r):

The radius (r) can be calculated using the formula: r = P / (2 * tan(θ))

Substitute the given perimeter (P) and angle (θ) into the formula: r = 16 / (2 * tan(120°))

Total Surface Area of the Cone:

The total surface area (A) of the cone can be calculated using the formula: A = πr(r + l)

Substitute the calculated values of r and l into the formula: A = π * 16 / (2 * tan(120°)) * (16 / (2 * tan(120°)) + 16 / (2 * π))

The total surface area of the cone can be calculated using the given information.

Let's calculate the values and provide the final answer.