the volume of the pans proper - presuming they are high enough to contain the batter - is irrelevant.
the baker is NOT making more and more and more batter to fill either the 9x13 or the two 9x9 pans to the brim.
when you pour X cubic inches into a pan of 117 square inches it will fill the pan to a depth = X divided by 117
if you pour the same volume of X cubic inches to one pan or five pans - equally - that in total are 162 square inches, the depth in each pan will be X divided by 162.
now, if X is the same number, is
X divided by 117
deeper or less deep than
X divided by 162
?
you are correct the volume of the batter is unknown. but the depth when equally split between the two 9x9 pans is not unknown.
it is (117/162=) 72.2% of the depth in the 9x13 pan.
