Solve for h v=1/3*(pir^2h)

$v = \frac{1}{3} \cdot (π r^{2} h)$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot (π r^{2} h) = v$ .

$\frac{1}{3} \cdot (π r^{2} h) = v$

Step 2

Multiply both sides of the equation by $\frac{1}{\frac{1}{3} π}$ .

$\frac{1}{\frac{1}{3} π} (\frac{1}{3} \cdot (π r^{2} h)) = \frac{1}{\frac{1}{3} π} v$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{1}{\frac{1}{3} π} (\frac{1}{3} \cdot (π r^{2} h))$ .

Combine $\frac{1}{3}$ and $π$ .

$\frac{1}{\frac{π}{3}} (\frac{1}{3} \cdot (π r^{2} h)) = \frac{1}{\frac{1}{3} π} v$

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{3}{π} (\frac{1}{3} \cdot (π r^{2} h)) = \frac{1}{\frac{1}{3} π} v$

Multiply $\frac{3}{π}$ by $1$ .

$\frac{3}{π} (\frac{1}{3} \cdot (π r^{2} h)) = \frac{1}{\frac{1}{3} π} v$

Cancel the common factor of $π$ .

Factor $π$ out of $\frac{1}{3} \cdot (π r^{2} h)$ .

$\frac{3}{π} (π (\frac{1}{3} \cdot (r^{2} h))) = \frac{1}{\frac{1}{3} π} v$

Cancel the common factor.

$\frac{3}{π} (π (\frac{1}{3} \cdot (r^{2} h))) = \frac{1}{\frac{1}{3} π} v$

Rewrite the expression.

$3 (\frac{1}{3} \cdot (r^{2} h)) = \frac{1}{\frac{1}{3} π} v$

Combine $r^{2}$ and $\frac{1}{3}$ .

$3 (\frac{r^{2}}{3} \cdot h) = \frac{1}{\frac{1}{3} π} v$

Combine $\frac{r^{2}}{3}$ and $h$ .

$3 \frac{r^{2} h}{3} = \frac{1}{\frac{1}{3} π} v$

Combine $3$ and $\frac{r^{2} h}{3}$ .

$\frac{3 (r^{2} h)}{3} = \frac{1}{\frac{1}{3} π} v$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (r^{2} h)}{3} = \frac{1}{\frac{1}{3} π} v$

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

$r^{2} h = \frac{1}{\frac{1}{3} π} v$

Simplify the right side.

Simplify $\frac{1}{\frac{1}{3} π} v$ .

Combine $\frac{1}{3}$ and $π$ .

$r^{2} h = \frac{1}{\frac{π}{3}} v$

Multiply the numerator by the reciprocal of the denominator.

$r^{2} h = 1 \frac{3}{π} v$

Multiply $\frac{3}{π}$ by $1$ .

$r^{2} h = \frac{3}{π} v$

Combine $\frac{3}{π}$ and $v$ .

$r^{2} h = \frac{3 v}{π}$

Step 4

Divide each term in $r^{2} h = \frac{3 v}{π}$ by $r^{2}$ and simplify.

Divide each term in $r^{2} h = \frac{3 v}{π}$ by $r^{2}$ .

$\frac{r^{2} h}{r^{2}} = \frac{\frac{3 v}{π}}{r^{2}}$

Simplify the left side.

Cancel the common factor of $r^{2}$ .

Cancel the common factor.

$\frac{r^{2} h}{r^{2}} = \frac{\frac{3 v}{π}}{r^{2}}$

Divide $h$ by $1$ .

$h = \frac{\frac{3 v}{π}}{r^{2}}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$h = \frac{3 v}{π} \cdot \frac{1}{r^{2}}$

Combine.

$h = \frac{3 v \cdot 1}{π r^{2}}$

Multiply $3$ by $1$ .

$h = \frac{3 v}{π r^{2}}$

Solve for h v=1/3*(pir^2h)

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