Final answer:
A birthmark caused by an increased volume of capillaries close to the surface of the skin is known as a vascular birthmark. Examples of vascular birthmarks include hemangiomas and port-wine stains.
Step-by-step explanation:
An example of a birthmark formed by the increased volume of capillaries close to the skin's surface is the port-wine stain, also known as nevus flammeus. This type of birthmark is characterized by reddish to purplish discoloration of the skin.
The birthmark occurs when capillaries (small blood vessels) beneath the skin’s surface become dilated or expanded. As a result, more blood flows through these vessels, and this increased volume of blood gives the birthmark its distinct color. Port-wine stains vary in size and can be found anywhere on the body. They are usually present at birth and often remain throughout life, potentially growing in size or darkening over time.