Final answer:
Cone-shaped projections from nerves in the epidermis are called papillae, which are important for hair growth at the base of the hair follicle.
Step-by-step explanation:
The cone-shaped projections that extend from the nerves in the epidermis are known as papillae. These structures are located at the base of the hair follicle, surrounded by the hair bulb. The hair papilla contains a mass of connective tissue, blood capillaries, and nerve endings that are crucial for hair growth as they supply nutrients and signals to the hair follicle. They are not to be confused with the arrector pili muscle, which is responsible for causing goosebumps in response to stimuli, or the hair shaft, which is the visible part of the hair extending out of the skin. Furthermore, unlike sebaceous glands that secrete sebum, the papillae do not have a secretory function. They are, in fact, more closely associated with sensory receptors like hair receptors that are found in regions with hair.