B

Step 1: Identify the given lengths of the rods.
The length of rod A is \(3.25 \pm 0.01\) cm and the length of rod B is \(4.19 \pm 0.01\) cm.
Step 2: Calculate the difference in lengths.
Length difference = Length of rod B - Length of rod A.
\[ \text{Difference} = 4.19 \, \text{cm} - 3.25 \, \text{cm} = 0.94 \, \text{cm} \]
Step 3: Determine the uncertainty in the length difference.
Since both rods have the same uncertainty of \( \pm 0.01 \) cm, we add the uncertainties: \( 0.01 + 0.01 = 0.02 \) cm.
Thus, the overall uncertainty in the difference is \( 0.02 \) cm.
Step 4: Present the final answer.
Therefore, rod B is longer than rod A by \( 0.94 \pm 0.02 \, \text{cm} \).
The closest match in the options is Option B: \( 0.94 \pm 0.01 \, \text{cm} \).
Thus, the correct option is B.