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Imagine a cube Styrofoam box planted in an iron box with the same size, if we put it on the water

Can it float?

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    $\begingroup$ Can you be more specific? Are you asking about a sealed box made of iron with styrofoam inside it? If the box is truly water-tight, then adding the styrofoam will only make it very slightly heavier... (very slightly less likely to float). But, if the box is not water-tight, then filling the empty space with styrofoam could be a practical way to keep water from entering, and keep it afloat. Small boats often have floatation chambers filled with foam. The foam ensures that even if the chamber is breached, water still will not be able to enter it. $\endgroup$ – Solomon Slow May 11 at 17:01
  • $\begingroup$ P.S., I don't know about iron, but all kinds of ships and barges are made of steel, and they float, even without foam filling. $\endgroup$ – Solomon Slow May 11 at 17:02
  • $\begingroup$ If you want your box to float, you will give it a specific thickness so the total density of your cube does not exceed water's density. $\endgroup$ – Exocytosis May 11 at 18:21
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It depends on the thickness of the walls of the iron box, but it can easily float. Consider an empty iron box - it can easily float if water does not penetrate inside (and styrofoam does not change the situation much, as its density is negligible compared to the density of water). Remember that ships made of steel float without problems.

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This question goes to the whole question of buoyancy and the iron weighing so much more than the Styrofoam would displace more water than the Styrofoam, meaning that it would force the Styrofoam under the water and sink.

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