Archimedes' principle

The AP Physics 1 CED states the content without using the name. Essential knowledge 8.3.B.3 reads that the magnitude of the buoyant force exerted on an object by a fluid is equivalent to the weight of the fluid displaced by the object. Learn the sentence; the label is just the traditional name for it.

Getting from the principle to the sheet equation takes one line. The displaced fluid has volume $V$ and density $\rho$, so its mass is $\rho V$ and its weight is $\rho V g$. Hence $F_b = \rho V g$.

The principle is more useful than the formula in two situations. First, a floating object displaces a weight of fluid equal to its own weight, full stop, which answers "how much water does this boat push aside" without touching volumes. Second, it explains why the water level in a glass does not change when a floating ice cube melts: the melted water has exactly the weight the floating cube was displacing.

The classic laboratory use runs the logic backwards. Weigh an irregular object in air and again while hanging submerged; the difference is $F_b$, which gives you the volume and then the density. The CED lists that as a suggested desktop experiment for topic 8.3.