Question

Чому дорівнює довжина найкоротшого маршруту мурашки вздовж ребер куба зі стороною 1 см, який починається і закінчується в одній і тій самій вершині?

Answer 1

Довжина найкоротшого маршруту мурашки вздовж ребер куба =12 см

Answer 2

Finding the Length of the Shortest Route for an Ant on a Cube

To find the length of the shortest route for an ant on a cube with a side length of 1 cm, starting and ending at the same vertex, we can use the concept of the space diagonal of a cube.

The space diagonal of a cube can be calculated using the formula: d = √(l^2 + w^2 + h^2), where l, w, and h are the length, width, and height of the cube.

Let's calculate the space diagonal of the cube with a side length of 1 cm.

Calculating the Space Diagonal

The space diagonal (d) of a cube with a side length of 1 cm can be calculated as follows: d = √(1^2 + 1^2 + 1^2) d = √(1 + 1 + 1) d = √3 d ≈ 1.732 cm

So, the length of the space diagonal of the cube is approximately 1.732 cm.

Conclusion

Therefore, the length of the shortest route for an ant on a cube with a side length of 1 cm, starting and ending at the same vertex, is approximately 1.732 cm.