Buoyant force?

Question

Just after it is lanched, a helium-filled research balloon resembles a thin vertical cigar. When it reaches n alttude of 50000 feet, it looks like a fat peach. The material of the balooon exerts no appreciable force on the gas within, but simply serves as a boundary separating air from hilium. Explain carefully why the buoyant force on the balloon remains constant as it rises.

Answer 1

I think that  as the balloon rises, the air around is less dense. Helium tries to move into area of lower density, hence the change in size of the balloon. The amount of Helium doesn't grow, it just tries harder to get out. So the air it displaces doesn't change. Now, the buoyant force equals the weight of the air displaced,

and since there is no change in the air displaced, the buoyant force doesn't change.