Question

Find a function that models the area A of a circle in terms of its circumference C.

Answer 1

Circumference

\[C = 2 \pi r\]

then \[r = C/2\pi\]

for the area

\[A=\pi r^2\]

or

\[A = \pi (C/2\pi)^2 = C^2 /4\pi\]

Answer 2

To add on, you have the area in terms of the radius. If you can turn the radius into some form of the circumference, then you have the area in terms of the circumference (which is what cambell did).

Answer 3

going the other way

\[r = \sqrt{A/\pi}\]

then
\[C = 2\pi \sqrt{A/\pi}\]