Question

У правильній трикутній піраміді бічне ребро утворює з площиною основи кут β. Знайти об’єм піраміди, якщо радіус кола, описаного навколо основи, дорівнює R.

Answer 1

Ответ:R^3 корень с 6/4

Объяснение:

Answer 2

Finding the Volume of a Right Triangular Pyramid

To find the volume of a right triangular pyramid, we can use the formula:

V = (1/3) * A_base * h

Where: - V = volume of the pyramid - A_base = area of the base - h = height of the pyramid

In this case, we are given that the lateral edge forms an angle β with the base. Additionally, the radius of the circle circumscribed around the base is given as R.

Solution

First, let's find the area of the base of the pyramid. Since the base is a circle, the area can be calculated using the formula for the area of a circle:

A_base = π * R^2

Next, we need to find the height of the pyramid. The height can be found using the formula:

h = R * cos(β)

Now, we can substitute the values into the volume formula:

V = (1/3) * (π * R^2) * (R * cos(β))

Final Answer

The volume of the pyramid is given by the formula:

V = (1/3) * π * R^3 * cos(β)

This formula provides the volume of the right triangular pyramid based on the given parameters.