Answer: The nearby nerve that can be affected by this tumour is the FACIAL NERVE.
Step-by-step explanation:
As stated in the question, the acoustic neuroma is a tumor that arises from the vestibular portion of the vestibulocochlear nerve which is the VIII ( 8th) cranial nerve.
VESTIBULOCOCHLEAR NERVE: These nerves are composed of two distinct sets of fibres, vestibular nerves and cochlear nerves.
The vestibular nerves arise from the semicircular canals of the inner ear and convey impulses to the cerebellum. They are associated with the maintenance of posture and balance. The cochlear nerves originate in the spiral organ in the inner ear and convey impulses to the hearing areas in the cerebral cortex where sound is perceived.
The Facial nerve, also called the 7th cranial nerve, which are the motor fibres that supply the muscles of facial expression. It lies adjacent to the vestibulocochlear nerve as they pass through the internal auditory canal which is located at the petrous part of the temporal bone. As the tumor grows, the facial nerve would be affected because it's the closest nerve to the VESTIBULOCOCHLEAR nerve..