The structure that is completely made of cartilage is
Epiglottis is a large, leaf-shaped piece of cartilage lying on top of the larynx, attached to the thyroid cartilage. Its unattached portion is free to move up and down to cover the glottis (vocal folds and rima glottidis) during swallowing.
Trachea has C-shaped cartilaginous rings but it also is composed of connective and epithelial tissue.
The nasal septum is the key midline support structure of the nose and is composed of the quadrilateral cartilage, perpendicular plate of the ethmoid bone, and vomer bone.
The pharynx is composed of mucous membrane, submucosal connective tissue, glands, lymphoid tissue, muscle and an outermost adventitial coating.