Since a circle is 2D it cannot have a surface area.
However, for the area of a circle
We know that and
Use substitution to get a formula for A in terms of C.
If you mean a sphere or a cylinder please reply
What has confused us [old timers] is pi a true or precise way of finding area of circle given that creating a square from it [morphing if you like] has a different area.
If everyday life us mere mortals have no use of pi, trigonometry and algebra. Will admit to using Pythagoras for finding squaring up a frame.
We watching a TV show on the story of maths and has got us fascinated.