Solve for h s=2pr^2+2prh

$s = 2 p r^{2} + 2 p r h$

Step 1

Rewrite the equation as $2 p r^{2} + 2 p r h = s$ .

$2 p r^{2} + 2 p r h = s$

Step 2

Subtract $2 p r^{2}$ from both sides of the equation.

$2 p r h = s - 2 p r^{2}$

Step 3

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

Divide each term in $2 p r h = s - 2 p r^{2}$ by $2 p r$ .

$\frac{2 p r h}{2 p r} = \frac{s}{2 p r} + \frac{- 2 p r^{2}}{2 p r}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 p r h}{2 p r} = \frac{s}{2 p r} + \frac{- 2 p r^{2}}{2 p r}$

Rewrite the expression.

$\frac{p r h}{p r} = \frac{s}{2 p r} + \frac{- 2 p r^{2}}{2 p r}$

Cancel the common factor of $p$ .

Cancel the common factor.

$\frac{p r h}{p r} = \frac{s}{2 p r} + \frac{- 2 p r^{2}}{2 p r}$

Rewrite the expression.

$\frac{r h}{r} = \frac{s}{2 p r} + \frac{- 2 p r^{2}}{2 p r}$

Cancel the common factor of $r$ .

Cancel the common factor.

$\frac{r h}{r} = \frac{s}{2 p r} + \frac{- 2 p r^{2}}{2 p r}$

Divide $h$ by $1$ .

$h = \frac{s}{2 p r} + \frac{- 2 p r^{2}}{2 p r}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 2$ and $2$ .

Factor $2$ out of $- 2 p r^{2}$ .

$h = \frac{s}{2 p r} + \frac{2 (- p r^{2})}{2 p r}$

Cancel the common factors.

Factor $2$ out of $2 p r$ .

$h = \frac{s}{2 p r} + \frac{2 (- p r^{2})}{2 (p r)}$

Cancel the common factor.

$h = \frac{s}{2 p r} + \frac{2 (- p r^{2})}{2 (p r)}$

Rewrite the expression.

$h = \frac{s}{2 p r} + \frac{- p r^{2}}{p r}$

Cancel the common factor of $p$ .

Cancel the common factor.

$h = \frac{s}{2 p r} + \frac{- p r^{2}}{p r}$

Rewrite the expression.

$h = \frac{s}{2 p r} + \frac{- 1 r^{2}}{r}$

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

Factor $r$ out of $- 1 r^{2}$ .

$h = \frac{s}{2 p r} + \frac{r (- 1 r)}{r}$

Cancel the common factors.

Raise $r$ to the power of $1$ .

$h = \frac{s}{2 p r} + \frac{r (- 1 r)}{r^{1}}$

Factor $r$ out of $r^{1}$ .

$h = \frac{s}{2 p r} + \frac{r (- 1 r)}{r \cdot 1}$

Cancel the common factor.

$h = \frac{s}{2 p r} + \frac{r (- 1 r)}{r \cdot 1}$

Rewrite the expression.

$h = \frac{s}{2 p r} + \frac{- 1 r}{1}$

Divide $- 1 r$ by $1$ .

$h = \frac{s}{2 p r} - 1 r$

Rewrite $- 1 r$ as $- r$ .

$h = \frac{s}{2 p r} - r$

Solve for h s=2pr^2+2prh

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