$\begingroup$The circumference of the circle is $C$, what is the area of circle in terms of $C$?
a). $\dfrac {C^2}{4\pi }$
b). $2\pi C$
c). $\dfrac {4}{3} \pi C^2$
d). $2\pi C^2$
My Attempt: $$\textrm {Circumference}=2\pi r$$ $$C=2\pi r$$ $$\dfrac {C}{2\pi }= r$$ Now, Area$=\pi r^2$ $$=\pi \dfrac {C^2}{4\pi^2}$$
$\endgroup$21 Answer
$\begingroup$Your attempt is correct, you should just cancel out the $\pi$ in the expression:
$$\require{cancel} \dfrac {\pi C^2}{4\pi^2} = \dfrac {\bcancel{\pi} C^2}{4 \bcancel{\pi} \pi} = \dfrac {C^2}{4\pi}$$
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