What is the volume of a black hole?
Our intuitive sense of volume breaks down in the strong gravitational region in a black hole. So while the “size” of a black hole is given by the radius of its event horizon, it’s volume is not determined by the usual 4/3*pi*r3. Instead, relativity makes it more complicated than that. As you pass the event horizon, the spatial direction ‘inwards’ becomes ‘towards the future’– you WILL reach the center, it’s as inevitable as next Monday. The direction outsiders think of as their future becomes a spatial dimension once you are inside. The volume of a black hole, therefore, is its surface area times the length of time the hole exists (using the speed of light to convert from seconds to meters). Since a black hole last practically forever, the black hole’s volume is almost infinite. (This is also a way of explaining the fact that you can pour stuff into a black hole forever and never fill it up.
