The correct explanation for why a hot air balloon rises when the air inside is heated is:
B. The hot air inside the balloon becomes less dense than the air outside the balloon.
When the air inside the balloon is heated, it expands, causing its density to decrease compared to the cooler, denser air outside the balloon. According to Archimedes' principle, an object (or balloon, in this case) will rise if it is less dense than the air surrounding it, which is exactly what happens when the air inside the balloon is heated.