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

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

Step 1

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

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

Step 2

Multiply both sides of the equation by $3$ .

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

Step 3

Simplify the left side.

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

Multiply $\frac{1}{3} (s^{2} h)$ .

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

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

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

$3 \frac{s^{2} h}{3} = 3 v$

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{s^{2} h}{3} = 3 v$

Rewrite the expression.

$s^{2} h = 3 v$

Step 4

Divide each term in $s^{2} h = 3 v$ by $s^{2}$ and simplify.

Divide each term in $s^{2} h = 3 v$ by $s^{2}$ .

$\frac{s^{2} h}{s^{2}} = \frac{3 v}{s^{2}}$

Simplify the left side.

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

Cancel the common factor.

$\frac{s^{2} h}{s^{2}} = \frac{3 v}{s^{2}}$

Divide $h$ by $1$ .

$h = \frac{3 v}{s^{2}}$