Is a solid ball bearing a 4 dimensional object, but all we see is one particular level surface?
When we look at a solid ball bearing, we can only see the outside of it, we cannot see inside even though there is more inside since it's solid, so we are only looking at a level surface.
A ball bearing is a 3-dimensional manifold with boundary, which is the most natural way of looking at it.
However, the 3-ball $B^3 = \{(x,y,z) \in \Bbb R^3 : x^2 + y^2 + z^2 \leq 1\}$ is a slice of the 4-ball $B^4 = \{(x,y,z,w)\in \Bbb R^4 : x^2 + y^2 + z^2 + w^2 \leq 1\}$; simply consider the intersection $B^4 \cap \Bbb R^3 = B^3$, where we're identifying $\Bbb R^3 = \{(x,y,z,0) \in \Bbb R^4\}$. (I don't think this is a particularly interesting way of thinking of a ball bearing, though.)