Question

В трехмерном пространстве рассматриваются кубы ребра которых параллельны координатным осям а координаты вершин этих кубов принимают целые значения от 0 до 5 каково число таких кубов осям а координаты вершин этих кубов

Answer 1

Методом аналогий  - 289

Answer 2

Number of Cubes with Integer Coordinates in 3D Space

In a three-dimensional space, cubes are considered with edges parallel to the coordinate axes, and the coordinates of the vertices of these cubes take integer values from 0 to 5. The task is to determine the number of such cubes.

To solve this problem, we can consider the number of cubes along each axis separately. Since the coordinates of the vertices of the cubes take integer values from 0 to 5, there are 6 possible positions for each edge along each axis (0, 1, 2, 3, 4, 5). Therefore, the total number of cubes along each axis is 6.

To find the total number of cubes, we can multiply the number of cubes along each axis together:

Total number of cubes = 6 * 6 * 6 = 216

This means that there are 216 such cubes in the three-dimensional space with the given conditions.