Question

ПОМОГИТЕ!!!! стороны основания прямоугольного параллелепипеда относятся как 2:4 а диагональное сечение представляет собой квадрат с площадью 225 см . найдите объем параллелепипеда

Answer 1

Согласно условию получается, что одна сторона основания в два раза больше другой
Поскольку сечение является квадратом, то DC₁=2a
Площадь квадрата
S=(2a)²=4a²
По условию
4a²=225
a²=225/4
a=15/2=7,5
По т.Пифагора найдем высоту
h²+a²=(2a)²
h²=4a²-a²
h²=3a²
h=a√3
Искомый объем
V=a*2a*h=2a²·a√3=2a³√3=2*7.5³√3=843,75√3

Answer 2

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Answer 3

Finding the Volume of a Rectangular Parallelepiped

To find the volume of a rectangular parallelepiped, we need to know the lengths of its sides. In this case, we are given that the sides of the base of the parallelepiped are in a ratio of 2:4. Let's assume the lengths of the sides are 2x and 4x, where x is a constant.

Now, we are also given that the diagonal cross-section of the parallelepiped is a square with an area of 225 cm². Since the diagonal of a square is equal to the side length multiplied by the square root of 2, we can find the length of the diagonal of the square cross-section.

Let's calculate the length of the diagonal of the square cross-section:

Step 1: Find the side length of the square cross-section. The area of the square cross-section is given as 225 cm². Therefore, the side length of the square can be found by taking the square root of the area: Side length = √(225 cm²) = 15 cm.

Step 2: Find the length of the diagonal of the square cross-section. The diagonal of a square is equal to the side length multiplied by the square root of 2: Diagonal = 15 cm * √2 ≈ 21.21 cm.

Now that we have the length of the diagonal of the square cross-section, we can use it to find the lengths of the sides of the parallelepiped.

Step 3: Find the lengths of the sides of the parallelepiped. The lengths of the sides of the parallelepiped are in a ratio of 2:4. Let's assume the lengths are 2x and 4x, where x is a constant.

We can set up the following equation using the Pythagorean theorem: (2x)² + (4x)² = (21.21 cm)².

Simplifying the equation: 4x² + 16x² = 449.94 cm², 20x² = 449.94 cm², x² = 22.497 cm², x ≈ 4.74 cm.

Therefore, the lengths of the sides of the parallelepiped are approximately: 2x ≈ 2 * 4.74 cm ≈ 9.48 cm, 4x ≈ 4 * 4.74 cm ≈ 18.96 cm.

Step 4: Find the volume of the parallelepiped. The volume of a rectangular parallelepiped is given by the formula: Volume = Length * Width * Height.

In this case, the lengths of the sides are approximately: Length ≈ 9.48 cm, Width ≈ 18.96 cm, Height is not given.

Since the height is not provided, we cannot calculate the exact volume of the parallelepiped. We need the height to complete the calculation.

Please provide the height of the parallelepiped so that we can find its volume.