Solve for r a=(pir^2)/h

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Algebra

$a = \frac{π r^{2}}{h}$

Rewrite the equation as $\frac{π r^{2}}{h} = a$ .

$\frac{π r^{2}}{h} = a$

Multiply both sides by $h$ .

$\frac{π r^{2}}{h} h = a h$

Simplify the left side.

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Cancel the common factor of $h$ .

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Cancel the common factor.

$\frac{π r^{2}}{h} h = a h$

Rewrite the expression.

$π r^{2} = a h$

Solve for $r$ .

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Divide each term in $π r^{2} = a h$ by $π$ and simplify.

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Divide each term in $π r^{2} = a h$ by $π$ .

$\frac{π r^{2}}{π} = \frac{a h}{π}$

Simplify the left side.

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Cancel the common factor of $π$ .

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Cancel the common factor.

$\frac{π r^{2}}{π} = \frac{a h}{π}$

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

$r^{2} = \frac{a h}{π}$

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

$r = \pm \sqrt{\frac{a h}{π}}$

Simplify $\pm \sqrt{\frac{a h}{π}}$ .

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Rewrite $\sqrt{\frac{a h}{π}}$ as $\frac{\sqrt{a h}}{\sqrt{π}}$ .

$r = \pm \frac{\sqrt{a h}}{\sqrt{π}}$

Multiply $\frac{\sqrt{a h}}{\sqrt{π}}$ by $\frac{\sqrt{π}}{\sqrt{π}}$ .

$r = \pm \frac{\sqrt{a h}}{\sqrt{π}} \cdot \frac{\sqrt{π}}{\sqrt{π}}$

Combine and simplify the denominator.

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Multiply $\frac{\sqrt{a h}}{\sqrt{π}}$ and $\frac{\sqrt{π}}{\sqrt{π}}$ .

$r = \pm \frac{\sqrt{a h} \sqrt{π}}{\sqrt{π} \sqrt{π}}$

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

$r = \pm \frac{\sqrt{a h} \sqrt{π}}{{\sqrt{π}}^{1} \sqrt{π}}$

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

$r = \pm \frac{\sqrt{a h} \sqrt{π}}{{\sqrt{π}}^{1} {\sqrt{π}}^{1}}$

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

$r = \pm \frac{\sqrt{a h} \sqrt{π}}{{\sqrt{π}}^{1 + 1}}$

Add $1$ and $1$ .

$r = \pm \frac{\sqrt{a h} \sqrt{π}}{{\sqrt{π}}^{2}}$

Rewrite ${\sqrt{π}}^{2}$ as $π$ .

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

$r = \pm \frac{\sqrt{a h} \sqrt{π}}{{(π^{\frac{1}{2}})}^{2}}$

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

$r = \pm \frac{\sqrt{a h} \sqrt{π}}{π^{\frac{1}{2} \cdot 2}}$

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

$r = \pm \frac{\sqrt{a h} \sqrt{π}}{π^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$r = \pm \frac{\sqrt{a h} \sqrt{π}}{π^{\frac{2}{2}}}$

Rewrite the expression.

$r = \pm \frac{\sqrt{a h} \sqrt{π}}{π^{1}}$

Simplify.

$r = \pm \frac{\sqrt{a h} \sqrt{π}}{π}$

Combine using the product rule for radicals.

$r = \pm \frac{\sqrt{a h π}}{π}$

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

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

$r = \frac{\sqrt{a h π}}{π}$

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

$r = - \frac{\sqrt{a h π}}{π}$

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

$r = \frac{\sqrt{a h π}}{π}$

$r = - \frac{\sqrt{a h π}}{π}$

$r = \frac{\sqrt{a h π}}{π}$

$r = - \frac{\sqrt{a h π}}{π}$

$r = \frac{\sqrt{a h π}}{π}$

$r = - \frac{\sqrt{a h π}}{π}$

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