why surface area of sphere is not equal to 2 * pi^2 * r^2 ?

Question

Pretty much the title, Cannot fathom why titled formula is invalid or not in use?
We take half the vertical cirucmference, pi * r and rotate it around the horizontal periphery on its axis, 2 * pi * r, this should give the value of surface area.

Pic just for reference –
https://qphs.fs.quoracdn.net/main-qimg-902ca0ec6c07471c700357a711f7e70c-c

In: Mathematics

Answer 1

>around the horizontal periphery on its axis, 2 * pi * r

That is only the distance it is rotating at its equator, not everywhere. Every point is going a different distance. What you are describing is a cylinder, no a sphere.