Solve for R A=piR^2-pir^2

$A = π R^{2} - π r^{2}$

Rewrite the equation as $π R^{2} - π r^{2} = A$ .

$π R^{2} - π r^{2} = A$

Add $π r^{2}$ to both sides of the equation.

$π R^{2} = A + π r^{2}$

Divide each term in $π R^{2} = A + π r^{2}$ by $π$ and simplify.

Divide each term in $π R^{2} = A + π r^{2}$ by $π$ .

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

Simplify the left side.

Cancel the common factor of $π$ .

Cancel the common factor.

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

Divide $R^{2}$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $π$ .

Cancel the common factor.

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

Divide $r^{2}$ by $1$ .

$R^{2} = \frac{A}{π} + r^{2}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$R = \pm \sqrt{\frac{A}{π} + r^{2}}$

Simplify $\pm \sqrt{\frac{A}{π} + r^{2}}$ .

To write $r^{2}$ as a fraction with a common denominator, multiply by $\frac{π}{π}$ .

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

Combine the numerators over the common denominator.

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

Rewrite $\sqrt{\frac{A + r^{2} π}{π}}$ as $\frac{\sqrt{A + r^{2} π}}{\sqrt{π}}$ .

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

Multiply $\frac{\sqrt{A + r^{2} π}}{\sqrt{π}}$ by $\frac{\sqrt{π}}{\sqrt{π}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{\sqrt{A + r^{2} π}}{\sqrt{π}}$ by $\frac{\sqrt{π}}{\sqrt{π}}$ .

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

Raise $\sqrt{π}$ to the power of $1$ .

$R = \pm \frac{\sqrt{A + r^{2} π} \sqrt{π}}{{\sqrt{π}}^{1} \sqrt{π}}$

Raise $\sqrt{π}$ to the power of $1$ .

$R = \pm \frac{\sqrt{A + r^{2} π} \sqrt{π}}{{\sqrt{π}}^{1} {\sqrt{π}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$R = \pm \frac{\sqrt{A + r^{2} π} \sqrt{π}}{{\sqrt{π}}^{1 + 1}}$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{π}}^{2}$ as $π$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{π}$ as $π^{\frac{1}{2}}$ .

$R = \pm \frac{\sqrt{A + r^{2} π} \sqrt{π}}{{(π^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$R = \pm \frac{\sqrt{A + r^{2} π} \sqrt{π}}{π^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$R = \pm \frac{\sqrt{A + r^{2} π} \sqrt{π}}{π^{1}}$

Simplify.

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

Combine using the product rule for radicals.

$R = \pm \frac{\sqrt{(A + r^{2} π) π}}{π}$

Reorder factors in $\pm \frac{\sqrt{(A + r^{2} π) π}}{π}$ .

$R = \pm \frac{\sqrt{π (A + r^{2} π)}}{π}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$R = \frac{\sqrt{π (A + r^{2} π)}}{π}$

Next, use the negative value of the $\pm$ to find the second solution.

$R = - \frac{\sqrt{π (A + r^{2} π)}}{π}$

The complete solution is the result of both the positive and negative portions of the solution.

$R = \frac{\sqrt{π (A + r^{2} π)}}{π}$

$R = - \frac{\sqrt{π (A + r^{2} π)}}{π}$

$R = \frac{\sqrt{π (A + r^{2} π)}}{π}$

$R = - \frac{\sqrt{π (A + r^{2} π)}}{π}$

Solve for R A=piR^2-pir^2

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