Final answer:
The structure that matches the given description is the larynx. It is composed partially of cartilage and plays a crucial role in the respiratory system.
Step-by-step explanation:
The structure that extends from the 3rd to 6th cervical vertebra, is attached to the hyoid bone, opens into the laryngopharynx, and is continuous with the trachea is the larynx.
The larynx, also known as the voice box, is involved in the production of sound and allows air to flow into the trachea. It is composed partially of cartilage and plays a crucial role in the respiratory system.