Solve for h v=1/3pi^2h

$v = \frac{1}{3} π^{2} h$

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

$\frac{1}{3} \cdot (π^{2} h) = v$

Multiply both sides of the equation by $\frac{1}{\frac{1}{3} π^{2}}$ .

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

Simplify both sides of the equation.

Simplify the left side.

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

Combine $\frac{1}{3}$ and $π^{2}$ .

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

Multiply the numerator by the reciprocal of the denominator.

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

Multiply $\frac{3}{π^{2}}$ by $1$ .

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

Cancel the common factor of $π^{2}$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Combine $\frac{1}{3}$ and $h$ .

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

Combine $3$ and $\frac{h}{3}$ .

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $h$ by $1$ .

$h = \frac{1}{\frac{1}{3} π^{2}} v$

Simplify the right side.

Simplify $\frac{1}{\frac{1}{3} π^{2}} v$ .

Combine $\frac{1}{3}$ and $π^{2}$ .

$h = \frac{1}{\frac{π^{2}}{3}} v$

Multiply the numerator by the reciprocal of the denominator.

$h = 1 \frac{3}{π^{2}} v$

Multiply $\frac{3}{π^{2}}$ by $1$ .

$h = \frac{3}{π^{2}} v$

Combine $\frac{3}{π^{2}}$ and $v$ .

$h = \frac{3 v}{π^{2}}$