"Continent" is not well-defined here. In particular, how deep do you go? To sea level?
To the base of the crust? To the base of the lithosphere?
Also, what constitutes a continent at the surface? You can find several different conceptions of what the continents are that are accepted in different contexts. For example, Europe and Asia are different to a Brit but the same to the Japanese. North and South America are different to the Canadians but the same continent to the Guatemalans. And what about nearby islands, and the continental shelf?
Once you define what counts as your continent, it becomes a pretty easy calculation because density of rock is more or less predictable as a function of depth.