If we extend that to 'a ballroom worthy of the name', I think the Imperator (1913) would be a strong contender. The ballroom on the Imperator was 74' long, 54' wide and 24' high to the top of its glass ceiling dome. Even the windows were 12' high. The German superliners of the Edwardian period were far more sumptuous than anything Cunard or White Star could offer, but even so a space of that size could not be reserved purely for occasional use, so the Imperator's ballroom had an everyday function as a 'social hall' (ie another lounge). When in ballroom mode (see below), the furniture covering the hardwood dance floor was shifted to the sides, where up to 100 people could choose to 'sit it out' while others danced.