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 po floating partly submerged in a fluid of density pf, the buoyant force is given by F = prg | A(y) dy, where g is the acceleration due to ' = Pf8 gravity and A (y) is the area of a typical cross-section of the object (see the figure). The weight of the object is given by W = po8 A (y) dy (a) Show that the percentage of the volume of the object above the surface of the liquid is 100LLL (b) The density of ice is 917 kg/m3 and the density of seawater is 1030 kg/m3. What percentage of the volume of an iceberg is above water? (c) An ice cube floats in a glass filled to the brim with water. Does the water overflow when the ice melts?

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 po floating partly submerged in a fluid of density pf, the buoyant force is given by F = prg | A(y) dy, where g is the acceleration due to ' = Pf8 gravity and A (y) is the area of a typical cross-section of the object (see the figure). The weight of the object is given by W = po8 A (y) dy (a) Show that the percentage of the volume of the object above the surface of the liquid is 100LLL (b) The density of ice is 917 kg/m3 and the density of seawater is 1030 kg/m3. What percentage of the volume of an iceberg is above water? (c) An ice cube floats in a glass filled to the brim with water. Does the water overflow when the ice melts?