Solve for h t=2rpih+2pir^2

$t = 2 r π h + 2 π r^{2}$

Rewrite the equation as $2 r π h + 2 π r^{2} = t$ .

$2 r π h + 2 π r^{2} = t$

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

$2 r π h = t - 2 π r^{2}$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $r$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $π$ .

Cancel the common factor.

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

Divide $h$ by $1$ .

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

Simplify the right side.

Simplify each term.

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

Factor $2$ out of $- 2 π r^{2}$ .

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

Cancel the common factors.

Factor $2$ out of $2 r π$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $π$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factors.

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $- 1 r$ by $1$ .

$h = \frac{t}{2 r π} - 1 r$

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

$h = \frac{t}{2 r π} - r$

Solve for h t=2rpih+2pir^2

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