Solve A=2pirh+2pir^2

$$A = 2 \pi r h + 2 \pi r ^ { 2 }$$

Solve for h

$$\left\{\begin{matrix}h=\frac{A-2\pi r^{2}}{2\pi r}\text{, }&r\neq 0\\h\in \mathrm{R}\text{, }&A=0\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$2\pi rh+2\pi r^{2}=A$$

Subtract 2\pi r^{2} from both sides.

$$2\pi rh=A-2\pi r^{2}$$

Divide both sides by 2\pi r.

$$\frac{2\pi rh}{2\pi r}=\frac{A-2\pi r^{2}}{2\pi r}$$

Dividing by 2\pi r undoes the multiplication by 2\pi r.

$$h=\frac{A-2\pi r^{2}}{2\pi r}$$

Divide A-2\pi r^{2} by 2\pi r.

$$h=-r+\frac{A}{2\pi r}$$

Solve for A

$$A=2\pi r\left(r+h\right)$$