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How do you calculate volume displaced in a fluid?

It depends on what information you have. If you know the volume of the object, and the object is completely submerged: then volume displaced is just the volume of the object. Sometimes you can figure out volume displaced by employing Archimedes' principle and/or static equilibrium. For example, suppose you have something floating on water, partially submerged. You know its weight, although maybe you don't know the volume submerged (which is the volume displaced). From Archimedes you know that the buoyant force is $\rho V_{\rm displ} g$. From static equilibrium you know that the weight is equal to this, i.e. $\rho V_{\rm displ} g = W$. We can then get that $V_{\rm displ}= \frac{W}{\rho g}$. For other problems, depending on the details, you may be able to set up various equations to get displaced volume.

Kate Scholberg 2015-04-07