Wikipedia records the dimensions as, "According to the blueprints, Serenity was laid down in August 2459. The ship is 269 feet (82 m) long bow to stern, with a 170 feet (52 m) beam, and stands 79 feet (24 m) high when landed."
I normally use Felix's old software to construct ships but I don't have it available at the moment so this is a rough take. If we go by those dimensions and not what we perceive by watching the show, then I think the Serenity is basically a cylinder, not counting the port and starboard engine protrusions. I took the radius to be half of the 24m when landed as the radius. I then took the height as the 82m length from bow to stern. Using formulas on the internet, I came up with 37,095.93 cubic meters or cumets. Looking at the Mass Table in Star Strike, it looks like this method shows a Heavy Freighter. I never thought of the Serenity as a Heavy Freighter, so I don't know if we should use the literal method for the ship. I haven't gone any further, since I need to think about it some more. I can't remember how much cargo tonnage the Serenity held on the show, but I don't remember the cargo hold being that big.
Good topic though. I like to think about these types of things.
