Final answer:
There are two sites for the EcoRI restriction enzyme in the circular DNA molecule.
Step-by-step explanation:
The number of sites for a restriction enzyme in a circular DNA molecule can be determined by analyzing the recognition sequence for that particular enzyme. Restriction enzymes are usually palindromic, meaning they read the same in the 5' to 3' direction on both strands. In the given information, the recognition sequence for EcoRI is 5'GAATTC3'. Since it is palindromic, this means that the complementary strand also has the same sequence, but in the opposite direction, 5'GAATTC3'. Therefore, there are two sites for this enzyme in the DNA molecule.