Final answer:
The volume must increase when the mass of an object increases in order for the density to remain the same. This is because density is mass divided by volume, so any change to the mass must be matched with a proportional change to the volume to maintain the same density.
Step-by-step explanation:
If the mass of an object increases, the volume must also increase for the density of the object to remain the same. Density is defined as the mass per unit volume of an object. Therefore, density is mathematically expressed as density = mass/volume. When mass increases, volume must increase proportionally to keep the density constant. This is because density is an intrinsic property of a material, representing how much mass is contained within a certain volume. If the volume doesn't change, but the mass does, the density will inevitably change.
To illustrate, imagine you have a piece of clay with a certain volume and mass, giving it a certain density. If you add more clay (thus adding more mass), you also increase the volume of the clay piece. If the increase in volume is proportional to the increase in mass, the density of the clay piece will remain the same. Conversely, if you added mass without increasing the volume, the clay piece would become denser.