Question

4. Осевое сечение усеченного конуса - равнобедренная трапеция, острый угол которой равен 60°, диагональ - 25 см и средняя линия - 24 см. Найдите площадь боковой поверхности усеченного конуса. Помогите пожалуйста!!!

Answer 1

Объяснение в файлах

Answer 2

Finding the Surface Area of a Truncated Cone

To find the surface area of a truncated cone, we can use the formula:

Surface Area = π(R + r)l

Where: - R = radius of the larger base - r = radius of the smaller base - l = slant height

Given Information

- The truncated cone is a right-angled cone with an acute angle of 60°. - The diagonal of the trapezoid is 25 cm. - The mean line (average of the two parallel sides) is 24 cm.

Calculating the Surface Area

First, we need to find the radii and the slant height of the truncated cone.

The formula for the diagonal of a trapezoid is given by: d = √(h^2 + (a - b)^2)

Where: - d = diagonal - h = height of the trapezoid - a and b = lengths of the parallel sides

From the given information, we can calculate the radii and the slant height using the properties of a trapezoid and a right-angled cone.

Calculations

1. Calculating the Radii: - Using the given mean line and the acute angle of the trapezoid, we can calculate the radii of the larger and smaller bases.

2. Calculating the Slant Height: - Once we have the radii, we can calculate the slant height using the Pythagorean theorem.

3. Finding the Surface Area: - Finally, we can use the formula for the surface area of a truncated cone to find the total surface area.

Let's calculate the values and find the surface area of the truncated cone.