Question

Rearrange the formula A = π(R2 − r2) for R.

Answer 1

Answer:

If you are doing it on USATestPrep, the answer is

D) R= Square root of  A over \pi and plus r^2    

The Square root goes all the way

I hope this helped ;)

Answer 2

ANSWER

$R = \pm \sqrt{\frac{A+\pi r^2}{ \pi}}$

EXPLANATION

We want to rearrange the formula,

$A=\pi(R^2-r^2)$
for
$R.$

This means that, we will isolate
$R$
so that, it will be on one side of the equation, while the others are also on the other side of the equation.

We must first divide through by π to obtain,

$\frac{A}{ \pi} =R^2-r^2$

We add
${r}^{2}$

to both sides to obtain,

$\frac{A}{ \pi} + {r}^{2} =R^2$

We now take the square root of both sides to obtain,

$\pm \sqrt{\frac{A}{ \pi} + {r}^{2}} =R$

We simplify further to obtain,

$R = \pm \sqrt{\frac{A+\pi r^2}{ \pi}}$