Solve v=1/3pir^2h

$$v = \frac { 1 } { 3 } \pi r ^ { 2 } h$$

Solve for h (complex solution)

$$\left\{\begin{matrix}h=\frac{3v}{\pi r^{2}}\text{, }&r\neq 0\\h\in \mathrm{C}\text{, }&v=0\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\frac{1}{3}\pi r^{2}h=v$$

The equation is in standard form.

$$\frac{\pi r^{2}}{3}h=v$$

Divide both sides by \frac{1}{3}\pi r^{2}.

$$\frac{3\times \frac{\pi r^{2}}{3}h}{\pi r^{2}}=\frac{3v}{\pi r^{2}}$$

Dividing by \frac{1}{3}\pi r^{2} undoes the multiplication by \frac{1}{3}\pi r^{2}.

$$h=\frac{3v}{\pi r^{2}}$$

Solve for h

$$\left\{\begin{matrix}h=\frac{3v}{\pi r^{2}}\text{, }&r\neq 0\\h\in \mathrm{R}\text{, }&v=0\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\frac{1}{3}\pi r^{2}h=v$$

The equation is in standard form.

$$\frac{\pi r^{2}}{3}h=v$$

Divide both sides by \frac{1}{3}\pi r^{2}.

$$\frac{3\times \frac{\pi r^{2}}{3}h}{\pi r^{2}}=\frac{3v}{\pi r^{2}}$$

Dividing by \frac{1}{3}\pi r^{2} undoes the multiplication by \frac{1}{3}\pi r^{2}.

$$h=\frac{3v}{\pi r^{2}}$$

Solve for r (complex solution)

$$\left\{\begin{matrix}r=-\left(\pi h\right)^{-\frac{1}{2}}\sqrt{3v}\text{; }r=\left(\pi h\right)^{-\frac{1}{2}}\sqrt{3v}\text{, }&h\neq 0\\r\in \mathrm{C}\text{, }&v=0\text{ and }h=0\end{matrix}\right.$$

Solve for r

$$\left\{\begin{matrix}r=\sqrt{\frac{3v}{\pi h}}\text{; }r=-\sqrt{\frac{3v}{\pi h}}\text{, }&\left(v\geq 0\text{ and }h>0\right)\text{ or }\left(v\leq 0\text{ and }h<0\right)\\r\in \mathrm{R}\text{, }&v=0\text{ and }h=0\end{matrix}\right.$$