Final answer:
The center of mass of an object can lie outside its physical boundaries, but for a uniformly made dice, it lies within. This concept applies to various shapes and systems, impacting factors such as stability and balance.
Step-by-step explanation:
The center of mass of an object does not necessarily have to coincide with actual material of the object and can sometimes lie outside its physical boundaries. One classic example of where the center of mass lies outside of the actual body is a doughnut-shaped object, also known as a torus. A dice, or cube, however, has its center of mass within the object itself, provided it is homogeneously made from a uniform material.
A good demonstration of the concept of the center of mass can be related to a seesaw. If you place different weights at varying distances from the pivot, you can calculate the center of mass of this system. Overall, the center of mass represents a weighted average position of all the mass in a system and is the point where you can model the system's mass as if it were all concentrated at that single point when considering external forces and torques.
The concept of a center of mass is critical in understanding the balance and stability of objects. In the context of trucks, for instance, the distribution of mass affects the location of the center of mass of the vehicle and hence its stability. For a hollow spherical object like a steel sphere, the center of mass is at its geometric center though it contains no actual mass at that point.