Final answer:
The rough endoplasmic reticulum (RER) typically has the largest surface area in a human secretory cell due to its extensive network of tubules and cisternae covered with ribosomes for protein synthesis.
Step-by-step explanation:
In a typical human secretory cell, the membrane with the largest surface area is the endoplasmic reticulum (ER), specifically the rough endoplasmic reticulum (RER). The RER has a structure that includes an interconnected array of tubules and cisternae, which significantly increases its surface area. The RER is studded with ribosomes, which produce proteins destined for various cellular destinations, including the plasma membrane. Proteins synthesized on the RER can enter the lumen or become part of the membrane itself. Vesicles budding from the RER may carry these proteins to the Golgi apparatus for processing or directly to the plasma membrane.
The smooth endoplasmic reticulum (SER), on the other hand, is involved in biosynthesis of lipids and several other functions but lacks ribosomes, contributing to a smoother appearance. The plasma membrane is another extensive structure, as it encases the entire cell; however, due to the extensive network and surface area covered by the RER within the cell, it is typically the RER that has the larger surface area. The lysosome and nuclear inner membrane have smaller surface areas compared to these extensive networks.