Question

The circumference of a circle whose area is $81{\mathrm{\pi r}}^2$, is

• A. $9\mathrm{\pi r}$
• B. $18\mathrm{\pi r}$
• C. $3\mathrm{\pi r}$
• D. $81\mathrm{\pi r}$

Answer 1

The correct option is B

$18\mathrm{\pi r}$

Let us assume R be the radius of circle

We know that, area of circle $\mathbf{=}\mathit{\pi }{\mathit{R}}^{\mathbf{2}}$

$$\begin{gathered} 81{\mathrm{\pi r}}^2={\mathrm{\pi R}}^2 \\ \mathrm{R}=\sqrt{81{\mathrm{r}}^2} \\ \mathrm{R}=9\mathrm{r} \end{gathered}$$

Circumference of the circle $\mathbf{=}\mathbf{2}\mathit{\pi }\mathit{R}$

$$\begin{gathered} =2\mathrm{\pi }\left(9\mathrm{r}\right) \\ =18\mathrm{\pi r} \end{gathered}$$

Thus , the circumference of a circle$18\mathrm{\pi r}$

Hence the correct option is (B)