Imagine that a 1 m3 cube was cut into 1 mm3 cubes, and these cubes were stacked tightly

Imagine that a 1 m3 cube was cut into 1 mm3 cubes, and these cubes were stacked tightly in one row. How long will the line be?

These tasks: V (volume of the original cube) = 1 m3; V1 (volume of one cube) = 1 mm3 (in SI system V1 = 1 * 10 ^ -9 m3).

1) Determine the number of cubes obtained: n = V / V1 = 1 / (1 * 10 ^ -9) = 10 ^ 9 cubes.

2) Determine the length of the edge of one obtained cube: V1 = a1 ^ 3, whence a1 = V1 ^ 1/3 = (1 * 10 ^ -9) ^ 1/3 = 0.001 m.

3) Calculate the length of the resulting line: L = n * a1 = 10 ^ 9 * 0.001 = 10 ^ 6 m or 1000 km.

Answer: The length of the received line is 1000 km.