If a cube axbxc can be said that it is a series of “c” squares axb stacked one top of another, then volume of cube is sum of areas of all the c squares
ab+ab+…. ab c times, so abc.
Similarly could a sphere of radius r can be seen as a series of circles stacked one over other each with increasing radius from 0 to r for the top and bottom halves of sphere independently.
In that case volume of sphere is the twice the sum of all the areas of those circles.