what is the name for the tube shaped part of a firearm that the bullet or shot travels through after the cartridge is fired?

Barrel

Explanation:

Barrel

It is the part of the gun,

Barrel is a long tube made up of metal, in which the bullet or the projectile goes after the firing is done.

Guns can have a variety of sizes of barrels.

longer barrel means, the bullet will hit the target more frequent.

Barrels have some grooves, in the spiral form, in the rifling.

Barrels which have grooves spin the projectile faster after exiting the gun.

Thereby making the projectile more accurate and stable.