Archimedes’ Principle states that the buoyant force on an object partially or fully submerged in a fluid is equal to the weight of the fluid that the object displaces. Thus, for an object of density floating partly submerged in a fluid of density , the buoyant force is given by
where g is the acceleration due to gravity and A(y) is the area of a typical cross-section of the object. The weight of the object is given by,
Show that the percentage of the volume of the object above the surface of the liquid is
.
