# Circle area question

• Sep 23rd 2010, 11:17 AM
MisterGreen
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 ?
• Sep 23rd 2010, 11:38 AM
e^(i*pi)
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.

• Sep 23rd 2010, 12:04 PM
MisterGreen
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, 12:17 PM
e^(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 $A = \pi r^2$ 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
• Sep 24th 2010, 07:12 AM
MisterGreen
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.