Question

The area of a circle of circumference C is

(a) $\frac{C^2}{4\pi }$ (b) $\frac{C^2}{2\pi }$ (c) $\frac{C^2}{\pi }$ (d) $\frac{4C^2}{\pi }$

Answer 1

Let r be the radius of the circle. Then
$C=2\pi r\Rightarrow r=\frac{C}{\mathit{2}\pi }$
Therefore
Area of circle = $\pi r^2=\pi {\left(\frac{C}{2\pi }\right)}^{\mathit{2}}=\frac{C^2}{4\pi }$
Hence, the correct option is (a).