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Although steel is about eight times more dense than water, what happens here is they take the steel and spread it out, where all that mass is distributed over a larger volume of water. Since the formula for density is mass divided by volume (D = m/V), what we have effectively done here is keep the mass, the top number, the same, while we increase the bottom number. So while steel has the superior density numbers when it is a solid block of steel, those density numbers change when the block is pressed into thinner sheets that cover a larger volume of water. Anything that is less than the density of water will float on top of the water. Another force to consider is that of buoyancy, which is a pushing-up force water has. When you put a certain mass of steel in the water, it displaces that much volume in water, which in turn pushes back up on the steel ship. This is why you can try to pick up a friend in the swimming pool, and they are seemingly as light as a feather! Out of the water, the feat is much more difficult.
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