If a cube can be construed as a series of squares stacked one upon the other, can a sphere be considered as a series of circles stacked one upon the other?

Question

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.

2*pi*[ r^2+(r-1)^2+……0)

In: 0

Answer 1

No, because it doesn’t hold true even for the cube.

A square is a 2D object and has no thickness. So you can put however many you like above each other and would get either

– all squares in the same place with still thickness 0 or
– the squares “stacked” on one another but with a gap, so no new object is formed

Even if you’d use infinetly many squares for the second option, there would still be an infitesimal small gap.