Which of the following methods uses Archimedes' principle of buoyancy?

The correct choice revolves around hydrostatic (underwater) weighing, which directly employs Archimedes' principle of buoyancy. This principle states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object. In the context of hydrostatic weighing, a person is weighed both in air and while submerged in water.

By comparing these two weights, the amount of water displaced (which correlates with body volume) can be calculated. From this information, body density can be derived, as density is mass divided by volume. This method is a well-established technique for estimating body composition, particularly for determining body fat percentage, based on the volume of water displaced.

In contrast, the other methods listed—such as bioelectrical impedance analysis, air displacement plethysmography, and skinfold measurement—do not utilize buoyancy principles or rely on the direct displacement of water to gauge body composition. Instead, they utilize different physiological metrics or calculations based on other forms of measurement, like electrical resistance or skinfold thickness, to estimate body fat. Thus, hydrostatic weighing is uniquely significant as it directly applies the concept put forth by Archimedes.