Why does a steel ship float even though a piece of steel dropped in the water sinks?

Answer 1

It's simple really. The steel ship floats because it is filled with air compartments which allow it to be less dense than the water. The steel piece does not have any air pockets/compartments meaning it is denser than water thus the steel piece sinks.
Big ship not metal all the way through. If you think of all of ship, it is mostly air with metal frame and skin of metal around it, so its average weight (density of entire thing times volume) much less than solid metal. If average weight less than weight of water of same size, then water heavier than it, water pushes it up, and it floats.
First of all, an object floats if its OVERALL density is less than the density of the fluid in which it is placed.(it can be shown)

The metal ship, due to the large pockets of air inside the ship, has a lower density than water.

The piece of metal has a higher density than water.

Thus, the piece of metal sinks while the metal ship floats.
A cruise ship has a lower density than compared to a coin as mass divided volume = density thus a lower density will allow the object to float.
Buoyant force says that the force an object is buoyed up with is equal to the weight of the water the object displaces. A cruise ship is large and displaces a lot of water so it is buoyed up with a large force. A coin is small and displaces very little water and therefore the buoyant force is very little.

Answer 2

A steel ship floats because it is designed to displace enough water to generate a buoyant force greater than its weight. When a piece of steel is dropped into the water, it sinks because its density is greater than that of the water, causing it to displace less water than its weight, leading to sinking.