The circumference of a circle whose area is 81 ^2, is: - Vidyadip

MCQ

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

A
$9\pi\text{r}$
✓
$18\pi\text{r}$
C
$3\pi\text{r}$
D
$81\pi\text{r}$

✓

Answer

Correct option: B.

$18\pi\text{r}$

Let the radius of circle be $R$
$\therefore$ Area of circle $=\pi\text{R}^2$
$\Rightarrow81\pi\text{r}^2=\pi\text{R}^2$
$\Rightarrow\text{R}=\sqrt{81\text{r}^2}$
$\Rightarrow\text{R}=9\text{r}$
Now, circumference of circle $=2\pi\text{R}=2\pi(9\text{r})=18\pi\text{r}$

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