Solve for h V=1/3*(pr^2h)

$V = \frac{1}{3} \cdot (p r^{2} h)$

Step 1

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

$\frac{1}{3} \cdot (p r^{2} h) = V$

Step 2

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot (p r^{2} h)) = 3 V$

Step 3

Simplify the left side.

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

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

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

$3 (\frac{p}{3} (r^{2} h)) = 3 V$

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

$3 (\frac{r^{2} p}{3} h) = 3 V$

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

$3 \frac{r^{2} p h}{3} = 3 V$

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{r^{2} p h}{3} = 3 V$

Rewrite the expression.

$r^{2} p h = 3 V$

Step 4

Divide each term in $r^{2} p h = 3 V$ by $r^{2} p$ and simplify.

Divide each term in $r^{2} p h = 3 V$ by $r^{2} p$ .

$\frac{r^{2} p h}{r^{2} p} = \frac{3 V}{r^{2} p}$

Simplify the left side.

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

Cancel the common factor.

$\frac{r^{2} p h}{r^{2} p} = \frac{3 V}{r^{2} p}$

Rewrite the expression.

$\frac{p h}{p} = \frac{3 V}{r^{2} p}$

Cancel the common factor of $p$ .

Cancel the common factor.

$\frac{p h}{p} = \frac{3 V}{r^{2} p}$

Divide $h$ by $1$ .

$h = \frac{3 V}{r^{2} p}$