Solve for h s=2(pir^2+pirh)

$s = 2 (π r^{2} + π r h)$

Step 1

Rewrite the equation as $2 (π r^{2} + π r h) = s$ .

$2 (π r^{2} + π r h) = s$

Step 2

Divide each term in $2 (π r^{2} + π r h) = s$ by $2$ and simplify.

Divide each term in $2 (π r^{2} + π r h) = s$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $π r^{2} + π r h$ by $1$ .

$π r^{2} + π r h = \frac{s}{2}$

Step 3

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

$π r h = \frac{s}{2} - π r^{2}$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $π$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $r$ .

Cancel the common factor.

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

Divide $h$ by $1$ .

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

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

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

Multiply $\frac{s}{2}$ by $\frac{1}{π r}$ .

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

Cancel the common factor of $π$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factors.

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $- 1 r$ by $1$ .

$h = \frac{s}{2 π r} - 1 r$

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

$h = \frac{s}{2 π r} - r$

Solve for h s=2(pir^2+pirh)

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