Want to know if there is a known formula for calculating the surface area of a circle using only the circumference as a given measurement ?
Since a circle is 2D it cannot have a surface area.
However, for the area of a circle
We know that $\displaystyle A=\pi r^2$ and $\displaystyle C = 2 \pi r \: \rightarrow \: r = \dfrac{C}{2\pi}$
Use substitution to get a formula for A in terms of C.
If you mean a sphere or a cylinder please reply
Ah right. The term Surface Area is largely used for the area on the surface of a 3D shape.
I did give you the equations $\displaystyle A = \pi r^2$ and $\displaystyle r = \dfrac{C}{2\pi}$
Thus $\displaystyle A = \pi \left(\dfrac{C}{2\pi}\right)^2$
You can simplify, given that there will be a pi term involved it is apparant that they won't have the same area
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.