Question

Express the area and circumference of a circle as functions of the circle's radius. Then express the area as a function of the circumference.

Answer 1

You have nothing?

Answer 2

I know that the formula for the area of a circle is \[A=pir ^{2}\] and the circumference is \[C=2pir\], but I don't know where to go from there.

Answer 3

Try some substitution. \(\dfrac{C}{2} = \pi r\)

\(A = \pi r \cdot r\)

Do you see it?

It MAY mean a function of the Circumference ONLY. That's only a little more annoying. Solve the Circumference equation for 'r' and substitute the whole thing.

Answer 4

so then it would be \[A=\pi r \times \frac{ C }{ 2\pi }\] which would then equal \[A=\frac{ Cr }{ 2 }\]

Answer 5

Well, maybe, but it may be more like this:

\(\dfrac{C}{2} = \pi r\; and \;\dfrac{C}{2\pi} = r\)

And this leads to \(A = \pi r^{2} = (\pi r)\cdot (r) = \dfrac{C}{2}\cdot\dfrac{C}{2\pi} = \dfrac{C^{2}}{4\pi} = \dfrac{1}{\pi}\cdot\left(\dfrac{C}{2}\right)^{2}\)

Various ways to write it.

Answer 6

alright cool. thank you!