Question

найдите площадь основания конуса, если его образующая равна 12 см, а угол при шершине осевого сечения равен 120 градусов

Answer 1

l=12 см

α=120°

S=?

 S=πr²

r=?

 sin½α=r/l

sin½*120=r/12

sin60=r/12

√3/2=r/12

2r=12√3

r=6√3 см

 S=π*(6√3)²

S=π*108

S=108π≈339 см²

Answer 2

108пи-ответ,высота 12/2 ,так как угол при основани осевого сечения 30 градусов,и далее используем теорему пифагора,чтобы найти радиус.потом формула площади круга

Answer 3

Calculating the Area of the Cone's Base

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

Area of the base of a cone = πr^2

Where: - π (pi) is a constant approximately equal to 3.14159 - r is the radius of the base of the cone

Finding the Radius of the Cone's Base

Given that the slant height (l) of the cone is 12 cm and the angle at the vertex of the axial section is 120 degrees, we can use trigonometric functions to find the radius (r) of the base of the cone.

Using the formula: r = l * sin(θ)

Where: - l is the slant height of the cone - θ is the angle at the vertex of the axial section

Calculating the Radius

Substituting the given values: r = 12 * sin(120°)

Using the trigonometric identity that sin(120°) = sin(180° - 120°) = sin(60°), we get: r = 12 * sin(60°)

Calculating the Area of the Base

Now that we have the radius (r), we can calculate the area of the base of the cone using the formula: Area of the base of a cone = πr^2

Substituting the value of r: Area of the base of the cone = π * (12 * sin(60°))^2

Calculating the value: Area of the base of the cone ≈ π * (12 * √3/2)^2

Area of the base of the cone ≈ π * (6√3)^2

Area of the base of the cone ≈ π * 36 * 3

Area of the base of the cone ≈ 108π

So, the area of the base of the cone is approximately 108π square centimeters.