Math experts: What is the relationship between adding constant increments of pancake batter and the radius of the pancake?

If you have a bunch of pancake batter and add batter to a flat surface in increments of a constant volume (say ¼ cup), it’s clear the increase in radius will become smaller with each additional ¼ cup of batter added. Is there a mathematical formula that captures this relationship? I’m using pancakes as a general example because they’re viscous, and it’s easy to visualize, but I’m mostly concerned with the abstract case.