Anons, i have finished college almost a decade ago and tying to remember some basic calculus.
Picrelated is a simple way to derive volume of a sphere by integration (R is the radius, r is the radius of current circular slice as we go through sphere on x axis)
Here's the question: why doesnt the same approach work with sphere surface?
Like instead of starting with pi * r^2 to get surface, we use 2*pi*r to get the length and then integrate that to get the surface. But the resulting integral is just a mess that doesnt give the correct answer.
Why is this approach not valid and instead you use a much more complex method involving arc length?
Picrelated is a simple way to derive volume of a sphere by integration (R is the radius, r is the radius of current circular slice as we go through sphere on x axis)
Here's the question: why doesnt the same approach work with sphere surface?
Like instead of starting with pi * r^2 to get surface, we use 2*pi*r to get the length and then integrate that to get the surface. But the resulting integral is just a mess that doesnt give the correct answer.
Why is this approach not valid and instead you use a much more complex method involving arc length?
