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Reading this question reminded me of an idea I once had, and I wonder whether it's feasible.
Imagine a hollow ball made of something strong, like steel. Imagine there is nothing inside; only vacuum.
Is there any size of ball and any available material such that, if you made a ball like this, it would float like a helium balloon? In other words, that the mass of the ball itself plus the (0) mass of the vacuum would be less than the mass of the air it displaces, making it bouyant?
I suspect there is no material strong and light enough, but I don't know how to do the calculations.
(It's fun to imagine these being used in fantastical bridges or airships, though I suppose a bridge would be unwise; you wouldn't want it to rise or sink when the weather changes.)