Question

основание пирамиды MABCD является квадрат с диагональю корень из 6 ребро MB перпендикулярно плоскости основания а угол между плоскостями ABC и AMD = 60градусов. Найти объем прамиды

Answer 1

AD=v"6/v"2=v''3.

MA=2v"3 (напротив угла 30 град. Боковая грань MBA)

MB=v"12-3=v"9=3.

V=1/3*Sосн*MB=1/3*3*3=3 cм^3.

Answer 2

Finding the Volume of Pyramid MABCD

To find the volume of pyramid MABCD, we can use the formula for the volume of a pyramid, which is given by:

Volume = (1/3) * Base Area * Height

First, we need to find the base area and the height of the pyramid.

Base Area of the Pyramid

The base of pyramid MABCD is a square with a diagonal of √6. To find the area of the square, we can use the formula:

Area = (Diagonal^2) / 2

Substituting the given value of the diagonal (√6), we get:

Area = (6) / 2 = 3

So, the base area of pyramid MABCD is 3 square units.

Height of the Pyramid

The height of the pyramid can be found using the given information that the edge MB is perpendicular to the base plane and the angle between the planes ABC and AMD is 60 degrees.

The height of the pyramid can be calculated using the formula:

Height = (Edge Length * sin(Angle))

Substituting the given values, we get:

Height = (Edge Length * sin(60°))

As the edge length is not provided, we need additional information to calculate the height.

Conclusion

To find the volume of pyramid MABCD, we need the length of edge MB to calculate the height. Once the edge length is provided, we can use the formulas mentioned above to calculate the volume of the pyramid.