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

The answer is ‘yes’, but the math for those circles is a little complicated.

But yes, you’ve essentially got stacked circles increasing in radius from a point to your given radius then decreasing again until you get another point, and boom, sphere. The rate at which your radius changes is important, though!

In the weeds:

Your circles’ radiuses need to change based on a sine function iirc in order to get a sphere instead of an hourglass, stacked cones, or some kind of spheroid.

Think circles of πr_c^2 where r_c = r_s * sine(h), then you’d have to do some calculus to sum them up based on limits of h.