Object B floats because it is less dense than object A. From the equation DENSITY = MASS / VOLUME, we can rearrange for VOLUME = MASS / DENSITY. Since mass is the same we can see that if density is small then volume must be large.
Archimedes' Principle states that
Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.
For an object to float in a liquid it has to be buoyed up by a force exerted by the liquid that is equivalent to the weight of the object.
Here object A and object B have the same mass, but they differ in their volume. As object A sinks, it can be inferred that the weight of the volume of alcohol displaced by object A less than the weight of the object. On the other hand, object B floats in the alcohol implying that the weight of alcohol displaced by object B is equal to the weight of the object.
We can conclude that object B has a larger volume compared to object A.