The required sprinkler density in a high-piled storage area is:

In high-piled storage areas, the required sprinkler density is critical to ensuring adequate fire protection. The answer of 0.25 gpm/sq. ft. is based on the guidelines set forth by the National Fire Protection Association (NFPA) standards for sprinklers. This density is established considering factors such as the storage material, the pilfer plan, and the height of storage, all of which play significant roles in determining the appropriate level of water application needed to suppress a potential fire effectively.

This specific density level ensures that there is sufficient water discharged to combat a fire in areas where combustible materials are stored at higher elevations, which may lead to more significant fire hazards. Each of the other options represents different water discharge rates, but they do not meet the requirements specified for high-piled storage areas, which are recognized for their potential to involve large quantities of stored materials that can quickly become involved in a fire scenario.