Question

Высота конуса равна 8 см, угол при вершине осевого сечения равен 60градусов. найти радиус конуса и площадь его осевого сечения.

Answer 1

$S = R*H$
{Если угол при вершине равен 60 градусов, то осевым сечением конуса будет равносторонний треугольник. Его сторона равна образующей, то есть 8 см. Тогда радиус основания равен половине стороны и равен 4 см.}
$2R=H$
$R= H/2$
$R=4$
$S = 4*8$
Досчитайте сами, ответ записывается в $cm^{2}$.

Answer 2

Problem Statement

We are given a cone with a height of 8 cm and an angle of 60 degrees at the vertex of its axial section. We need to find the radius of the cone and the area of its axial section.

Solution

To find the radius of the cone, we can use the formula:

Radius of cone = Height of cone * tan(angle at vertex of axial section)

Let's calculate the radius using this formula:

Radius of cone = 8 cm * tan(60 degrees)

Using a calculator, we find that the tangent of 60 degrees is approximately 1.732. Therefore, the radius of the cone is:

Radius of cone = 8 cm * 1.732 ≈ 13.856 cm Now, let's find the area of the axial section of the cone. The axial section of a cone is a circle. The area of a circle can be calculated using the formula:

Area of circle = π * (Radius of circle)^2

Since the axial section of the cone is a circle with the radius we just calculated, we can find its area using this formula:

Area of axial section = π * (Radius of cone)^2

Substituting the value of the radius we found earlier, we get:

Area of axial section = π * (13.856 cm)^2

Using a calculator, we find that the square of 13.856 is approximately 191.13. Therefore, the area of the axial section of the cone is:

Area of axial section ≈ π * 191.13 cm^2 ≈ 600.97 cm^2

Answer

The radius of the cone is approximately 13.856 cm, and the area of its axial section is approximately 600.97 cm^2.