To find out how much sugar Aminah will need for 2.25 batches of the recipe, we can multiply the amount of sugar needed for one batch by the number of batches.
The amount of sugar for one batch is 2.5 cups. Therefore:
\[ \text{Total sugar} = \text{Sugar per batch} \times \text{Number of batches} \] \[ \text{Total sugar} = 2.5 , \text{cups} \times 2.25 \]
Now, perform the multiplication:
\[ 2.5 \times 2.25 = 5.625 \]
So, Aminah will need 5.625 cups of sugar.
The correct answer is B. 5.625 cups.