Question

Как наиболее коротким путём по поверхности куба ребро которого равно 2 дм Муравей может добраться из одной его вершины в противоположную? Чему равен этот путь ?

Answer 1

Сама олимпиаду выполняй)))

Answer 2

Finding the Shortest Path Across a Cube

To find the shortest path across the surface of a cube with an edge length of 2 dm, we can consider the properties of a cube and the possible paths a ant could take to travel from one vertex to the opposite vertex.

The shortest path across the surface of a cube from one vertex to the opposite vertex is along the space diagonal of the cube. The space diagonal of a cube can be calculated using the formula:

Space Diagonal (d) = √(l^2 + w^2 + h^2)

Where: - l, w, and h are the length, width, and height of the cube, which are all equal in the case of a cube.

Substituting the given edge length of the cube (2 dm) into the formula, we get:

Space Diagonal (d) = √(2^2 + 2^2 + 2^2) Space Diagonal (d) = √(4 + 4 + 4) Space Diagonal (d) = √12 Space Diagonal (d) ≈ 3.46 dm

Therefore, the shortest path across the surface of the cube, from one vertex to the opposite vertex, is approximately 3.46 dm. This is the distance a ant would need to travel to reach the opposite vertex of the cube along the shortest path.