Final answer:
The volume of a balloon affects whether it will float or sink in the air, based on Archimedes' principle. If the buoyant force acting on the balloon, which is equal to the weight of the air displaced, is greater than the weight of the balloon, the balloon will float. Otherwise, it will sink.
Step-by-step explanation:
Density plays a crucial role in Archimedes' principle. The average density of an object determines whether it floats or sinks. If the average density of an object is less than the density of the surrounding fluid, it will float. On the other hand, if the average density is greater than the density of the fluid, it will sink.
The buoyant force on an object is equal to the weight of the fluid it displaces. The volume of the fluid displaced by the object is directly related to the volume of the object. When an object is submerged in a fluid, it displaces a volume of fluid equal to its own volume. This volume is used to calculate the buoyant force on the object.
For a balloon in the air, the volume works in a similar way. When the balloon is in the air, it displaces a volume of air equal to its own volume. The buoyant force acting on the balloon is equal to the weight of the air displaced.
If this buoyant force is greater than the weight of the balloon, the balloon will rise and float in the air. If the buoyant force is less than the weight of the balloon, the balloon will sink. So, the volume of the balloon determines the amount of air it displaces and thus affects whether it will float or sink.