1. ## Circle area question

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 ?

2. Since a circle is 2D it cannot have a surface area.

However, for the area of a circle

We know that $A=\pi r^2$ and $C = 2 \pi r \: \rightarrow \: r = \dfrac{C}{2\pi}$

Use substitution to get a formula for A in terms of C.

3. We wanted to know if for example if a circle with a circumference of say 28cm would have the same area as a square whose sides are 7cm?

Thus the perimeter measurement of each shape would be the same

Would area be the same?

4. 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 $A = \pi r^2$ and $r = \dfrac{C}{2\pi}$

Thus $A = \pi \left(\dfrac{C}{2\pi}\right)^2$

You can simplify, given that there will be a pi term involved it is apparant that they won't have the same area

5. 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.