Question

Образующая конуса наклонена к плоскости под углом 30 градусов, а высота равна 12см. Найти Sбок и V.

Answer 1

Всё решаем по формулам..................

Answer 2

Given Information:

We are given the following information about a cone: - The cone's axis is inclined to the plane at an angle of 30 degrees. - The height of the cone is 12 cm.

Finding the Slant Height (Sбок):

To find the slant height of the cone, we can use the formula:

Sбок = √(h^2 + r^2)

where: - Sбок is the slant height - h is the height of the cone - r is the radius of the base of the cone

Since the problem does not provide the radius of the base, we need to find it using the given information.

Finding the Radius (r):

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

r = h * tan(θ)

where: - θ is the angle between the axis of the cone and the plane

Substituting the given values, we have: - θ = 30 degrees - h = 12 cm

Using the formula, we can calculate the radius (r).

Calculating the Slant Height (Sбок):

Now that we have the radius (r), we can calculate the slant height (Sбок) using the formula mentioned earlier.

Finding the Volume (V):

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

V = (1/3) * π * r^2 * h

where: - V is the volume of the cone - π is a mathematical constant approximately equal to 3.14159 - r is the radius of the base - h is the height of the cone

Substituting the given values, we can calculate the volume (V).

Calculation:

Let's calculate the values step by step.

1. Finding the Radius (r): Using the formula r = h * tan(θ), where θ = 30 degrees and h = 12 cm: - r = 12 cm * tan(30 degrees) - r ≈ 6.928 cm

2. Calculating the Slant Height (Sбок): Using the formula Sбок = √(h^2 + r^2), where h = 12 cm and r ≈ 6.928 cm: - Sбок = √(12 cm^2 + (6.928 cm)^2) - Sбок ≈ √(144 cm^2 + 47.94 cm^2) - Sбок ≈ √(191.94 cm^2) - Sбок ≈ 13.86 cm

3. Finding the Volume (V): Using the formula V = (1/3) * π * r^2 * h, where π ≈ 3.14159, r ≈ 6.928 cm, and h = 12 cm: - V = (1/3) * 3.14159 * (6.928 cm)^2 * 12 cm - V ≈ (1/3) * 3.14159 * 47.94 cm^2 * 12 cm - V ≈ (1/3) * 3.14159 * 575.28 cm^3 - V ≈ 603.19 cm^3

Answer:

Therefore, the slant height (Sбок) of the cone is approximately 13.86 cm, and the volume (V) of the cone is approximately 603.19 cm^3.