And that's just it. You're relating the volume of the weapons to the volume of the hole. But you don't know anything about the volume of the weapon. What you do know is the weight. And that's where density comes into play. That's exactly the use of density, relating weight and volume.
Is the density of the swords exactly 490? Of course not. Is it a reasonable guess? I think so. Notice my use of "about", "approximate" and "guess". I'm not claiming exact numbers, but I'm willing to bet they're pretty close.