Which of the following structures is an example of a risk category III building?

A K-12 school with over 250 students qualifies as a risk category III building primarily due to its occupancy type and the potential consequences of its failure during a significant event, such as an earthquake or severe storm. Risk category III structures are those that house gatherings of people or are essential for public welfare and safety, which includes educational facilities that accommodate a considerable number of students.

In this context, such buildings are designed to sustain greater loading conditions and provide more significant structural integrity compared to lower-risk buildings. Therefore, they must meet stricter codes to ensure the safety of a potentially large group of occupants during emergencies, as the loss of life or injury in such settings could be substantial.

The other options, while potentially important structures, do not align with the criteria for risk category III. A private residence, low-occupancy storage facility, and a rural community center typically occupy different risk categories based on their expected occupancy and potential impact on community safety in case of structural failure.