Final answer:
The hollow shell made of gold will have a larger moment of inertia about an axis through its center compared to the solid aluminum sphere.
Step-by-step explanation:
The moment of inertia of an object depends on its mass distribution and the axis of rotation. In this case, we have two spheres with the same radius and mass, but one is solid aluminum while the other is a hollow shell of gold. The moment of inertia of a solid sphere is given by (2/5) * mass * radius², while the moment of inertia of a hollow sphere is given by (2/3) * mass * radius². Since the moment of inertia of a hollow sphere is greater than that of a solid sphere for the same mass and radius, the hollow sphere made of gold will have a larger moment of inertia about an axis through its center compared to the solid aluminum sphere.