Solve for h S=2pir(h+r)

$S = 2 π r (h + r)$

Rewrite the equation as $2 π r (h + r) = S$ .

$2 π r (h + r) = S$

Divide each term in $2 π r (h + r) = S$ by $2 π r$ and simplify.

Divide each term in $2 π r (h + r) = S$ by $2 π r$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $π$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $r$ .

Cancel the common factor.

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

Divide $h + r$ by $1$ .

$h + r = \frac{S}{2 π r}$

Subtract $r$ from both sides of the equation.

$h = \frac{S}{2 π r} - r$