Solve A=2pir^2+pirh

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

Solve for h (complex solution)

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

Steps for Solving Linear Equation

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

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

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

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

Divide both sides by \pi r.

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

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

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

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

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

Solve for h

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

Steps for Solving Linear Equation

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

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

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

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

Divide both sides by \pi r.

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

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

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

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

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

Solve for A

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