Solve for h v=pi/3*(r^2h)

$v = \frac{π}{3} \cdot (r^{2} h)$

Step 1

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

$\frac{π}{3} \cdot (r^{2} h) = v$

Step 2

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

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

Step 3

Simplify both sides of the equation.

Simplify the left side.

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

Multiply $\frac{π}{3} (r^{2} h)$ .

Combine $r^{2}$ and $\frac{π}{3}$ .

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

Combine $\frac{r^{2} π}{3}$ and $h$ .

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

Combine.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{r^{2} π h}{π} = \frac{3}{π} v$

Cancel the common factor of $π$ .

Cancel the common factor.

$\frac{r^{2} π h}{π} = \frac{3}{π} v$

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

$r^{2} h = \frac{3}{π} v$

Simplify the right side.

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=pi/3*(r^2h)

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