D&D 3.5e: How exactly do you calculate changing a Line into a Cone?

Exactly as the title is asking. But to be more specific, I am asking for the purposes of the Shape Breath Metabreath feat. As the feat says:

If you have a line-shaped breath weapon, you can opt to shape it into a cone. Likewise, if you have a cone-shaped breath weapon, you can shape it into a line. When you use this feat, add +1 to the number of rounds you must wait before using your breath weapon again.

Comparing this to the breath weapon of a Dragonborn of Bahamut, which is a Line with a range of 5ft per hit die, how would you calculate converting the breath weapon into a cone? Would a 6th-level Dragonborn of Bahamut breath out a 30ft cone? Or would the length of the cone be reduced?