Question

If the numerical value of the area of a circle is equal to the numerical value of its circumference , find its radius.

Answer 1

Given that area of the circle = circumference
$$\begin{gathered} {\mathrm{\pi r}}^2=2\mathrm{\pi r} \\ \Rightarrow {\mathrm{\pi r}}^2-2\mathrm{\pi r}=0 \\ \Rightarrow \mathrm{\pi r}\left(\mathrm{r}-2\right)=0 \\ \Rightarrow \mathrm{r}=0\mathrm{or}\mathrm{r}=2 \end{gathered}$$
Since radius cannot be equal to 0 so, r = 2