Final answer:
An Inside Micrometer is the hole inspection device that employs extension rods attached to a head for measuring the internal dimensions of holes.
Step-by-step explanation:
The hole inspection device that uses extension rods attached to a head is known as an Inside Micrometer. This tool is designed to measure the interior dimensions of objects. The inside micrometer consists of a calibrated screw and a spindle attached to a head that can be adjusted for length using interchangeable anvil rods (or extension rods). A variety of extension rods can be used to check different sizes of holes. The user selects the appropriate rod, attaches it to the micrometer head, and then adjusts the head until the rod makes contact with the sides of the hole being measured. The measurement is then read from the scale on the micrometer barrel.