3 ms·
As an aside, if you take the area of a circle, A = pi r^2, and take the derivative wrt r, you get the circumference 2 pi r. Similarly, the derivative of the vol
by FabHK 7y ago
As an aside, if you take the area of a circle, A = pi r^2, and take the derivative wrt r, you get the circumference 2 pi r. Similarly, the derivative of the volume of a sphere, V = 4/3 pi r^3, is the surface area A = 4 pi r^2.
It's sort of obvious, when you think about it, but it wasn't obvious to me before thinking about it :-)
- stevefan1999 7y agoYeah, back when I was first introduced to calculus and integration, I was surprised to see ∫4pir^2 dr = 4pi ∫r^2 dr = 4pi*r^3/3. Then I learnt about the Cavalieri's principle and it comes clear in mind.
- ColinWright 7y agoIt's cool ... I mention that in a different (but related) post here: https://www.solipsys.co.uk/new/ConsideringASphere.html#toc_name003 https://www.solipsys.co.uk/new/ConsideringASphere.html#toc_n...
- fctorial 7y agoIsn't it the case that integral of surface area is volume, that seems more obvious to me. The derivative happens to be reverse of integral and hence area happens to be derivative of volume.