In this link https://www.3blue1brown.com/lessons/essence-of-calculus Grant Sanderson said if we unwrapped the ring we can get the shape as depicted below. : 
, but i made a straight strip (physically) like that and tried wrapping it up to make a ring but problem was that some parts were not effectively matching with the ring structure and whenever i tried to make it more look like ring a bit of the strip of paper will tear out . (dr here represent finite thickness not tending to zero one ) as Grant said there
- So my question is why do we say that we can approximate the area of ring to be as a rectangle as such converting it to that form is physically not possible as i tried it , some parts bulges and some parts doesnt makes the ring structure at all ?
- And similarily why is that for spherical shell to we argue it to be approximately a cuboid type for calcuting volume ? As similarly to what i observed from ring its possible that there will be some deformation while converting it to cuboid shape isnt ?
Why i asked is because i think is that unwrapping it(ring) is not possible as such since its not at all will look like a straight line . I might guess that straight line strip with diagonal edges is different from ring structure , its not possible to convert into each other.
- Note : Assume we dont know the formula for area of circle and volume of sphere at all . We are as such trying to derive those from the approximations . Those approximations validity proof i needed why we assume so , given the wrongness i posted above in doing so .