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 ?

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- Sep 23rd 2010, 10:17 AMMisterGreenCircle 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 ?

- Sep 23rd 2010, 10:38 AMe^(i*pi)
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 - Sep 23rd 2010, 11:04 AMMisterGreen
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? - Sep 23rd 2010, 11:17 AMe^(i*pi)
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 - Sep 24th 2010, 06:12 AMMisterGreen
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.