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

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

Solve for h

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

$$r\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3r.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

Subtract 2\pi from both sides.

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

The equation is in standard form.

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

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

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

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

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

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

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

Solve for V

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

$$r\neq 0$$