Solve for r V=pir^2h for r

$V = π r^{2} h$ for $r$

Rewrite the equation as $π r^{2} h = V$ .

$π r^{2} h = V$

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

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

$\frac{π r^{2} h}{π h} = \frac{V}{π h}$

Simplify the left side.

Cancel the common factor of $π$ .

Cancel the common factor.

$\frac{π r^{2} h}{π h} = \frac{V}{π h}$

Rewrite the expression.

$\frac{r^{2} h}{h} = \frac{V}{π h}$

Cancel the common factor of $h$ .

Cancel the common factor.

$\frac{r^{2} h}{h} = \frac{V}{π h}$

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

$r^{2} = \frac{V}{π h}$

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

$r = \pm \sqrt{\frac{V}{π h}}$

Simplify $\pm \sqrt{\frac{V}{π h}}$ .

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

$r = \pm \frac{\sqrt{V}}{\sqrt{π h}}$

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

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

Combine and simplify the denominator.

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Rewrite ${\sqrt{π h}}^{2}$ as $π h$ .

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Combine using the product rule for radicals.

$r = \pm \frac{\sqrt{V π h}}{π h}$

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.

$r = \frac{\sqrt{V π h}}{π h}$

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

$r = - \frac{\sqrt{V π h}}{π h}$

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

$r = \frac{\sqrt{V π h}}{π h}$

$r = - \frac{\sqrt{V π h}}{π h}$

$r = \frac{\sqrt{V π h}}{π h}$

$r = - \frac{\sqrt{V π h}}{π h}$

Solve for r V=pir^2h for r

Related Questions

Support LCMGCF.com by disabling your adblocker.