Final answer:
A cube that has all edges expanding at a constant rate remains a cube, with its size increasing but its shape and proportions preserved.
Step-by-step explanation:
If all edges of a cube are expanding at a constant rate, the shape remains a cube. As each edge grows at the same rate, the shape does not become distorted; it simply becomes a larger cube. The cube continues to maintain its characteristic of equal edge lengths and 90° angles between its faces.
Even when considering geometric transformations that classify shapes based on movements such as rotations, the cube's characteristics remain unaffected by uniform expansion.
According to Figure 1.7 and Figure 13.11 in the provided data, when a three-dimensional object such as a cube expands, all three dimensions (length, width, height) increase.
This means the area of each face increases because both length and width increase, and the volume increases because length, width, and height increase, preserving the cube's proportions.