Solve for l S=2pirl+2pir^2

$S = 2 π r l + 2 π r^{2}$

Step 1

Rewrite the equation as $2 π r l + 2 π r^{2} = S$ .

$2 π r l + 2 π r^{2} = S$

Step 2

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

$2 π r l = S - 2 π r^{2}$

Step 3

Divide each term in $2 π r l = S - 2 π r^{2}$ by $2 π r$ and simplify.

Divide each term in $2 π r l = S - 2 π r^{2}$ by $2 π r$ .

$\frac{2 π r l}{2 π r} = \frac{S}{2 π r} + \frac{- 2 π r^{2}}{2 π r}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 π r l}{2 π r} = \frac{S}{2 π r} + \frac{- 2 π r^{2}}{2 π r}$

Rewrite the expression.

$\frac{π r l}{π r} = \frac{S}{2 π r} + \frac{- 2 π r^{2}}{2 π r}$

Cancel the common factor of $π$ .

Cancel the common factor.

$\frac{π r l}{π r} = \frac{S}{2 π r} + \frac{- 2 π r^{2}}{2 π r}$

Rewrite the expression.

$\frac{r l}{r} = \frac{S}{2 π r} + \frac{- 2 π r^{2}}{2 π r}$

Cancel the common factor of $r$ .

Cancel the common factor.

$\frac{r l}{r} = \frac{S}{2 π r} + \frac{- 2 π r^{2}}{2 π r}$

Divide $l$ by $1$ .

$l = \frac{S}{2 π r} + \frac{- 2 π r^{2}}{2 π r}$

Simplify the right side.

Simplify each term.

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

Factor $2$ out of $- 2 π r^{2}$ .

$l = \frac{S}{2 π r} + \frac{2 (- π r^{2})}{2 π r}$

Cancel the common factors.

Factor $2$ out of $2 π r$ .

$l = \frac{S}{2 π r} + \frac{2 (- π r^{2})}{2 (π r)}$

Cancel the common factor.

$l = \frac{S}{2 π r} + \frac{2 (- π r^{2})}{2 (π r)}$

Rewrite the expression.

$l = \frac{S}{2 π r} + \frac{- π r^{2}}{π r}$

Cancel the common factor of $π$ .

Cancel the common factor.

$l = \frac{S}{2 π r} + \frac{- π r^{2}}{π r}$

Rewrite the expression.

$l = \frac{S}{2 π r} + \frac{- 1 r^{2}}{r}$

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

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

$l = \frac{S}{2 π r} + \frac{r (- 1 r)}{r}$

Cancel the common factors.

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

$l = \frac{S}{2 π r} + \frac{r (- 1 r)}{r^{1}}$

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

$l = \frac{S}{2 π r} + \frac{r (- 1 r)}{r \cdot 1}$

Cancel the common factor.

$l = \frac{S}{2 π r} + \frac{r (- 1 r)}{r \cdot 1}$

Rewrite the expression.

$l = \frac{S}{2 π r} + \frac{- 1 r}{1}$

Divide $- 1 r$ by $1$ .

$l = \frac{S}{2 π r} - 1 r$

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

$l = \frac{S}{2 π r} - r$

Solve for l S=2pirl+2pir^2

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