Question

Найдите объем прямого параллелепипеда, если его основание имеет стороны 3 м и 4 м,угол между ними 30°,а одна из диагоналей параллелепипеда имеет длину 6 м и образует с плоскостью основания угол 30°

Answer 1

V=S*H
Против угла в 30°лежит катет равный половине гипотенузы⇒H=3
V=3*4*sin30°*3=18(м³)
Ответ:18.

Answer 2

Calculation of the Volume of a Rectangular Parallelepiped

To find the volume of a rectangular parallelepiped, we need to know the dimensions of its base and the angle between them, as well as the length of one of its diagonals.

Given: - Length of one side of the base: 3 m - Length of another side of the base: 4 m - Angle between the sides of the base: 30° - Length of one of the diagonals: 6 m - Angle between the diagonal and the plane of the base: 30°

To calculate the volume of the rectangular parallelepiped, we can use the formula:

Volume = Base Area × Height

The base area can be calculated using the formula:

Base Area = Side1 × Side2 × sin(Angle)

Let's calculate the base area first:

Base Area = 3 m × 4 m × sin(30°)

To calculate the height, we can use the formula:

Height = Diagonal × sin(Angle)

Now, let's calculate the height:

Height = 6 m × sin(30°)

Finally, we can calculate the volume:

Volume = Base Area × Height

Now, let's calculate the volume of the rectangular parallelepiped.

Calculation:

Base Area: - Side1 = 3 m - Side2 = 4 m - Angle = 30°

Base Area = 3 m × 4 m × sin(30°)

Height: - Diagonal = 6 m - Angle = 30°

Height = 6 m × sin(30°)

Volume: Volume = Base Area × Height

Now, let's calculate the values.

Solution:

Base Area: Base Area = 3 m × 4 m × sin(30°)

Height: Height = 6 m × sin(30°)

Volume: Volume = Base Area × Height

Using the given values and performing the calculations, we find:

Base Area = 6 m² Height = 3 m Volume = 6 m² × 3 m = 18 m³

Therefore, the volume of the rectangular parallelepiped is 18 cubic meters.

Please note that the calculations provided are based on the given information and assumptions. If there are any additional details or requirements, please let me know.