To calculate the cost of the large box containing 50 bottles of assorted drinks, you can multiply the price per bottle by the total number of bottles:
\[ \text{Total Cost} = \text{Price per bottle} \times \text{Number of bottles} \]
\[ \text{Total Cost} = 2.25 \times 50 \]
\[ \text{Total Cost} = 112.5 \]
Therefore, the large box costs $112.50.