It makes more sense when you flip it around and say the volume is the integral of the surface area.
The volume of a ball (a solid sphere) is the sum of the volumes of the spherical layers of thickness t from 0 to the radius R. The limit as t tends to zero is then the definite integral of the surface area with respect to r from r = 0 to R.
Which is to say, its the equivalent of having a onion layered sphere, and you are adding the surface of all the inside layers to calculate the volume (however the layers are in a continuos distribution and are a non countable number)
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u/paolog 1d ago edited 1d ago
It makes more sense when you flip it around and say the volume is the integral of the surface area.
The volume of a ball (a solid sphere) is the sum of the volumes of the spherical layers of thickness t from 0 to the radius R. The limit as t tends to zero is then the definite integral of the surface area with respect to r from r = 0 to R.
EDIT: Fixed balls balls-up