Question

Образующая конуса равна корень из 6 см и составляет с плоскостью основания угол 45 градусов Найти V конуса. с рисунком пожалуйста

Answer 1

Вот вам полное решение этой задачи

Answer 2

Calculating the Volume of a Cone

To find the volume (V) of a cone, we can use the formula:

V = (1/3) * π * r^2 * h

Where: - r is the radius of the base of the cone - h is the height of the cone

Given that the radius of the cone is equal to the square root of 6 cm and the angle between the generating line of the cone and the plane of its base is 45 degrees, we can calculate the volume of the cone.

Calculation

First, we need to find the height of the cone. Since the angle between the generating line and the plane of the base is 45 degrees, we can use trigonometric functions to find the height.

Using the given information, we can calculate the height (h) of the cone using the formula:

h = r * tan(θ)

Where: - r is the radius of the base of the cone - θ is the angle between the generating line of the cone and the plane of its base

Given that the radius (r) is the square root of 6 cm and the angle (θ) is 45 degrees, we can calculate the height.

h = √6 * tan(45°)

Using the value of tan(45°) = 1, we get:

h = √6 * 1 = √6 cm

Now that we have the height, we can calculate the volume of the cone using the formula:

V = (1/3) * π * r^2 * h

Substituting the values: V = (1/3) * π * (√6)^2 * √6 V = (1/3) * π * 6 * √6 V = 2π√6 cm^3

So, the volume of the cone is 2π√6 cubic centimeters.

Conclusion

The volume of the given cone is 2π√6 cubic centimeters.