Question

If the circumference of a circle measures 3/4 π cm, what is the area of the circle in terms of π?

Answer 1

$\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ -----\\ C=\frac{3\pi }{4} \end{cases}\implies \cfrac{3\pi }{4}=2\pi r \\\\\\ \cfrac{3\pi }{4(2\pi )}=r\implies \boxed{\cfrac{3}{8}=r}\\\\ -------------------------------\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad \implies A=\pi \left( \boxed{\frac{3}{8}} \right)^2\implies A=\pi \left( \cfrac{3^2}{8^2} \right) \\\\\\ A=\cfrac{9\pi }{64}$