I think my surprise is this: Would it be possible to cut a hole in one sphere, so that another sphere of the same size could pass through?
No, no way. The only way a sphere could pass through another sphere of the same size would be if the hole were exactly as big as the sphere, so you wouldn’t have any original sphere left.
So at first blush it seemed surprising that a cube could have a hole in it big enough for another cube of the same size – and even a little bigger! – to pass through. But then you realize that this is because, at specific angles, you could draw a square in a cube’s silhouette that is larger than any one of its sides.
When put like that, it doesn’t seem so surprising, but I think that speaks to our assumptions when first picturing the problem.
