What was the main purpose of the archaeologists who first investigated the old temples? What is the plural of sarcophagus?

The correct answer to this open question is the following.

Although you did not clarify what kind of temples among the many ancient temples you are referring to, we can say the following.

The main purpose of the archaeologists who first investigated the old temples, in general, was to dig in deeply to know the purpose of the temples, why the temples were built in the first place, what was his main use, how ancient people built temples with the lack of proper technology or tools, and how these old temples had endured the test of time.

Even to this modern-days, scientists and archeologists do not have a true and definitive statement about pyramids, temples, ziggurats, and other ancient temples and sites, it is just theories.

And regarding your second question, the plural of the word sarcophagus is sarcophagi.

i confess that there are several parts of this constitution which i do not at present approve, but i am not sure i shall never approve them: for having lived long, i have experienced many instances of being obliged by better information or fuller consideration, to change opinions even on important subjects, which i once thought right, but found to be otherwise. it is therefore that the older i grow, the more apt i am to doubt my own judgment, and to pay more respect to the judgment of others.