MCQ
If $\text{A}=\pi(\text{R}^2-\text{r}^2)$ than R is equal to.
  • A
    $\sqrt{\frac{\text{A}-\pi\text{r}^2}{\pi}}$
  • $\sqrt{\frac{\text{A}+\pi\text{r}^2}{\pi}}$
  • C
    $\sqrt{\frac{\text{r}^2\pi-\text{A}}{\pi}}$
  • D
    $\sqrt{\frac{\text{r}^2\pi-\text{A}}{\text{r}}}$

Answer

Correct option: B.
$\sqrt{\frac{\text{A}+\pi\text{r}^2}{\pi}}$

Given, $\text{A}=\pi(\text{R}^2-\text{r}^2)$
Therefore $\text{A}=\pi\text{R}^2-\pi\text{r}^2\Rightarrow\text{A}+\pi\text{r}^2=\pi\text{R}^2$
$\Rightarrow\text{R}^2={\frac{\text{A}+\pi\text{r}^2}{\pi}}$
$\Rightarrow\text{R}=\sqrt{\frac{\text{A}+\pi\text{r}^2}{\pi}}$

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