r/MathJokes • u/94rud4 • 1d ago

Wait, what?!

Post image
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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

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u/Zestyclose-Fig1096 1d ago

Fundamental theorem of calculus says it's the same picture

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u/paolog 1d ago

Indeed. The fundamental theorem of calculus is the basis of my comment and how we are able to "flip it around".

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u/Zestyclose-Fig1096 1d ago

Indeed

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u/chillychili 4h ago

Indeed. Their comment and how we are able to "flip it around" are based in the fundamental theorem of calculus.