Question

Express the circumference of a circle, C, as a function of its area, A.

Answer 1

\[C = 2 \pi r\]\[A = \pi r^2\]Solve latter equation for \(r\) in terms of \(A\) and substitute into the first equation.
\[\frac{A}{\pi} = r^2\]\[r = \sqrt{\frac{A}{\pi}}\]
you do the substitution and I'll check it

Answer 2

\[C=2\pi \sqrt{\frac{ A }{ \pi }}\]

Answer 3

Good job.

Answer 4

You can further reduce that as follows.

\[\large C = 2 \times \ \cancel{\sqrt{\pi}} \times \sqrt{\pi} \times \frac{\sqrt{A}}{
\cancel{\sqrt{\pi}}} = 2\sqrt{A \pi}\]