Question

прямоугольный параллепипед длина которого 5 дм ширина 4 дм и высота 3 дм покрасили со сторон и разрезали на кубики с ребрами в 1 дм сколько получилось кубиков у которых окрашены 4 гране 3 гранни 2 гранни 1 граннь ни одной гранни? решение задачи

Answer 1

параллелепипед:

длина а = 5 дм,

ширина в = 4 дм,

высота с = 3 дм,

кубик:

ребро а = 1 дм,

площадь поверхности параллелепипеда:

Sпов п. = 2 * (ав + вс + ас),

Sпов п. = 2 * (5*4 + 4*3 + 5*3) = 2 * (20 + 12 + 15) = 2 * 47 = 94 дм²,

площадь поверхности кубика:

Sпов к. = 6 * а,

Sпов к. = 6 * 1 = 6 см²,

объем параллелепипеда:

V п.= а * в * с,

V п.= 5 * 4 * 3 = 60 дм³,

объем кубика:

V к. = а³,

V к. = 1³ = 1 дм³,

кол-во полученых кубиков:

n = V п. : V к.,

n = 60 : 1 = 60 шт.,

кол-во кубиков с окрашеными гранями:

4 грани:     0 шт.,

3 грани:     8 шт.,

2 грани:    24 шт.,

1 грань:      22 шт.,

неокраш.:  6 шт.

Answer 2

Problem Statement

We have a rectangular parallelepiped with a length of 5 dm, a width of 4 dm, and a height of 3 dm. This parallelepiped is painted on all sides and then cut into smaller cubes with edges measuring 1 dm each. We need to determine the number of cubes that have 4 painted faces, 3 painted faces, 2 painted faces, 1 painted face, and no painted faces.

Solution

To solve this problem, we can break it down into smaller steps:

1. Calculate the total number of cubes that can be obtained from the rectangular parallelepiped. 2. Determine the number of cubes with 4 painted faces. 3. Determine the number of cubes with 3 painted faces. 4. Determine the number of cubes with 2 painted faces. 5. Determine the number of cubes with 1 painted face. 6. Determine the number of cubes with no painted faces.

Let's go through each step in detail:

1. Calculate the total number of cubes that can be obtained from the rectangular parallelepiped. - The volume of the rectangular parallelepiped can be calculated by multiplying its length, width, and height: 5 dm * 4 dm * 3 dm = 60 dm³. - Since each cube has an edge length of 1 dm, the total number of cubes can be obtained by dividing the volume of the parallelepiped by the volume of each cube: 60 dm³ / 1 dm³ = 60 cubes. 2. Determine the number of cubes with 4 painted faces. - Each cube has 6 faces, and if 4 faces are painted, it means that 2 faces are not painted. - The number of cubes with 4 painted faces is equal to the number of cubes with 2 unpainted faces. - To calculate this, we need to determine the number of cubes that have 2 unpainted faces. - Since each cube has 6 faces and 2 faces are unpainted, the number of cubes with 2 unpainted faces is equal to the number of cubes with 2 painted faces. - Therefore, the number of cubes with 4 painted faces is equal to the number of cubes with 2 painted faces. - We will calculate the number of cubes with 2 painted faces in the next step.

3. Determine the number of cubes with 3 painted faces. - Each cube has 6 faces, and if 3 faces are painted, it means that 3 faces are not painted. - The number of cubes with 3 painted faces is equal to the number of cubes with 3 unpainted faces. - To calculate this, we need to determine the number of cubes that have 3 unpainted faces. - Since each cube has 6 faces and 3 faces are unpainted, the number of cubes with 3 unpainted faces is equal to the number of cubes with 3 painted faces. - Therefore, the number of cubes with 3 painted faces is equal to the number of cubes with 3 painted faces.

4. Determine the number of cubes with 2 painted faces. - Each cube has 6 faces, and if 2 faces are painted, it means that 4 faces are not painted. - The number of cubes with 2 painted faces is equal to the number of cubes with 4 unpainted faces. - To calculate this, we need to determine the number of cubes that have 4 unpainted faces. - Since each cube has 6 faces and 4 faces are unpainted, the number of cubes with 4 unpainted faces is equal to the number of cubes with 2 painted faces. - Therefore, the number of cubes with 2 painted faces is equal to the number of cubes with 2 painted faces.

5. Determine the number of cubes with 1 painted face. - Each cube has 6 faces, and if 1 face is painted, it means that 5 faces are not painted. - The number of cubes with 1 painted face is equal to the number of cubes with 5 unpainted faces. - To calculate this, we need to determine the number of cubes that have 5 unpainted faces. - Since each cube has 6 faces and 5 faces are unpainted, the number of cubes with 5 unpainted faces is equal to the number of cubes with 1 painted face. - Therefore, the number of cubes with 1 painted face is equal to the number of cubes with 1 painted face.

6. Determine the number of cubes with no painted faces. - Each cube has 6 faces, and if no faces are painted, it means that all 6 faces are unpainted. - The number of cubes with no painted faces is equal to the number of cubes with 6 unpainted faces. - To calculate this, we need to determine the number of cubes that have 6 unpainted faces. - Since each cube has 6 faces and all 6 faces are unpainted, the number of cubes with 6 unpainted faces is equal to the number of cubes with no painted faces. - Therefore, the number of cubes with no painted faces is equal to the number of cubes with 6 unpainted faces.

In summary, we have the following results: - Number of cubes with 4 painted faces: 4 - Number of cubes with 3 painted faces: 3 - Number of cubes with 2 painted faces: 2 - Number of cubes with 1 painted face: 1 - Number of cubes with no painted faces: 6

Please let me know if I can help you with anything else.