In this case, there are 10 identical cells connected in series, so the total potential difference across the circuit is \( 10E \).
The internal resistance of the circuit is also 10 times the internal resistance of a single cell, i.e., \( 10r \).
When an ideal voltmeter is connected across three cells, it has infinite resistance and draws negligible current. As a result, the potential difference across the voltmeter will be the same as the potential difference across the three cells.
Since the three cells are connected in series, the potential difference across them is \( 3E \). Therefore, the voltmeter will read \( 3E \).
Thus, the correct answer is: (D) \( 3E \).