If 3x1x1 is the minimum size mikveh that an average person can fit in, and it also has the volume of 40 s'ah. Why would I need a full 40 s'ah of water?
If this Mikveh is big enough for a full body, the persons body will displace a certain amount of water out of the 3x1x1 container like tosfos on 4a and Rashi in sukkah 6a explain by e r'vies of wine for a Nahzir that we measure it based on the displaced wine.
So however much water is displaced out of the 3x1x1 Mikveh should be able to be subtracted from the 40 s'ah ?
Azarya
The Gemara (Eruvin 4b) tells us that a person's body can totally immerse in 3 X 1 X 1, and that the Sages estimated that this is equivalent to the volume of 40 Se'ah. So the certain amount of water that the person's body will displace is 40 Se'ah. 40 Se'ah is the volume of the average body.
Kol Tuv,
Dovid Bloom