The shortest distance the ant must travel to get to the opposite corner of the cube is the length of the space diagonal of the cube. To calculate the space diagonal, we can use the 3D Pythagorean theorem, which states that the length of the diagonal is the square root of the sum of the squares of the side lengths. In this case, since all the sides of the cube have the same length, let’s say the side length is s.
The space diagonal (shortest distance) is given by:
$$d = \sqrt{s^2 + s^2 + s^2}$$
Simplifying the equation:
$$d = \sqrt{3s^2}$$
In general terms, for a cube of side length s, the shortest distance between opposite corners (space diagonal) is given by:
$$d = s\sqrt{3}$$