What surrounds a muscle fibre and is known as the membranous sheath?

The sarcolemma is the correct answer because it functions as the plasma membrane of a muscle fiber. It plays a crucial role in maintaining the internal environment of the muscle cell, regulating the entry and exit of ions and nutrients, and facilitating communication with the rest of the muscle tissue. This membrane is essential for the proper function of muscle fibers, especially in the transmission of electrical signals that trigger muscle contraction.

In contrast, myofibrils are the contractile elements within a muscle fiber, composed of repeating units called sarcomeres. Endomysium refers to the connective tissue that surrounds individual muscle fibers, providing structural support and helping to transmit the force generated during contraction. Perimysium, on the other hand, is the connective tissue sheath that encases a group of muscle fibers, forming a fascicle. While all these structures are important in the anatomy of muscle tissue, the sarcolemma specifically designates the membrane that directly encloses the muscle fiber.