Why does a ship made of steel (denser than water) float?

Archimedes' principle (3rd century BC): a body fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. An object floats when the buoyant force equals its weight. A solid block of steel has density ~7,850 kg/m³, much denser than water (1,000 kg/m³); it sinks. But a steel SHIP is mostly hollow — its overall average density (steel + air inside + cargo) is LESS than water. As the ship sits in water, it displaces water; the buoyant force pushes up. The ship sinks deeper until enough water is displaced for the buoyant force to equal the ship's total weight. Then it floats in equilibrium. Loading more cargo: ship displaces more water (sits lower), buoyant force increases, equilibrium maintained until maximum capacity. Plimsoll line (load line): marking on ships indicating the maximum safe loading depth. Variables affecting buoyancy: (1) Fluid density — same object floats higher in dense water (salt water) than in fresh water; ships displace less salt water for the same buoyant force (which is why ships have different load lines for fresh and salt water); (2) Object density — less dense objects float higher or float entirely; (3) Object shape — shape affects how much fluid is displaced (a flat steel sheet sinks; the same steel formed into a bowl shape floats). Submarines control buoyancy by changing internal volume (ballast tanks fill with water to sink, empty to rise). Hot air balloons use the same principle in air (warm air less dense than cold air → buoyancy). Hydrometers measure fluid density by how deep they sink.