Solve V=pir^2h+2/3pir^3

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

Solve for h (complex solution)

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

Steps for Solving Linear Equation

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

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

Subtract \frac{2}{3}\pi r^{3} from both sides.

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

The equation is in standard form.

$$\pi r^{2}h=-\frac{2\pi r^{3}}{3}+V$$

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

$$\frac{\pi r^{2}h}{\pi r^{2}}=\frac{-\frac{2\pi r^{3}}{3}+V}{\pi r^{2}}$$

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

$$h=\frac{-\frac{2\pi r^{3}}{3}+V}{\pi r^{2}}$$

Divide V-\frac{2\pi r^{3}}{3} by \pi r^{2}.

$$h=-\frac{2r}{3}+\frac{V}{\pi r^{2}}$$

Solve for h

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

Steps for Solving Linear Equation

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

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

Subtract \frac{2}{3}\pi r^{3} from both sides.

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

The equation is in standard form.

$$\pi r^{2}h=-\frac{2\pi r^{3}}{3}+V$$

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

$$\frac{\pi r^{2}h}{\pi r^{2}}=\frac{-\frac{2\pi r^{3}}{3}+V}{\pi r^{2}}$$

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

$$h=\frac{-\frac{2\pi r^{3}}{3}+V}{\pi r^{2}}$$

Divide V-\frac{2\pi r^{3}}{3} by \pi r^{2}.

$$h=-\frac{2r}{3}+\frac{V}{\pi r^{2}}$$

Solve for V

$$V=\frac{\pi \left(2r+3h\right)r^{2}}{3}$$