What happens when the batter is declared out for hitting a ball outside the batter's box?

When a batter is declared out for hitting a ball outside the batter's box, the correct outcome is that the ball is dead, and the batter is out. This situation occurs when the batter makes contact with the pitch while not within the confines of the batter's box. According to the rules of baseball, hitting a ball while outside the batter's box is considered a violation, and as a direct consequence, the play cannot continue—thus, the ball is ruled dead.

Understanding this rule is crucial for umpires, as it ensures the game is played fairly and according to the established guidelines. The dead ball call also prevents any confusion regarding base runners or continuation of play following such an incident. In contrast, the other options indicate scenarios where the play could continue or where the batter might not be penalized, which does not align with the specific rule regarding contact made outside the batter's box.