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Saturn (the planet) would float if you could find anything large enough for it to float in.

The density of Saturn is 0.687 g/cm³ which is less than water.

However, the density of Saturn (the planet) is always calculated as the "mean density", indicating that the mass of the core, water, and gasses are all combined to provide the total mass of the planet, and the volume, including the gas mantle is used to calculate mean density. Naturally the gas mantle will float, since it is significantly less dense than water, but if the planet were placed in a theoretical container of water, the gas would no longer be a significant part of the process, and the core of the planet would sink.

So... it depends on how you're deciding whether the planet will float. Are you putting a large balloon around it then putting it into the theoretical container of water? Yes, it will float if that's what you're doing. But if the gas of the planet is allowed to act as a gas, everything changes... you decide.

Saturn (the vehicle) would float briefly, while the windows and doors are closed, but as air is displaced, water would fill the inside of the vehicle and it would sink.

If you wanted to fill the interior with beach balls or something else that would hold air... it would probably float.

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