Question

Find the area of a circle whose circumference is 8π. [CBSE 2014]

Answer 1

Let the radius of the circle be r.
​Now,
$$\begin{gathered} \mathrm{Circumference}=8\mathrm{\pi } \\ \Rightarrow 2\mathrm{\pi }r=8\mathrm{\pi } \\ \Rightarrow r=4\mathrm{cm} \end{gathered}$$
Now, Area of circle= $\mathrm{\pi }{r}^2=\mathrm{\pi }\times 4^2=16\mathrm{\pi }{\mathrm{cm}}^2$
Hence, the area of the circle is 16π cm².