Solve 5159/6=pir^2(h+2/3r)

$$\frac { 5159 } { 6 } = \pi r ^ { 2 } ( h + \frac { 2 } { 3 } r )$$

Solve for h

$$h=-\frac{2r}{3}+\frac{5159}{6\pi r^{2}}$$

$$r\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply \pi r^{2} by h+\frac{2}{3}r.

$$\frac{5159}{6}=\pi r^{2}h+\frac{2}{3}\pi r^{3}$$

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

$$\pi r^{2}h+\frac{2}{3}\pi r^{3}=\frac{5159}{6}$$

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

$$\pi r^{2}h=\frac{5159}{6}-\frac{2}{3}\pi r^{3}$$

The equation is in standard form.

$$\pi r^{2}h=-\frac{2\pi r^{3}}{3}+\frac{5159}{6}$$

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

$$\frac{\pi r^{2}h}{\pi r^{2}}=\frac{-\frac{2\pi r^{3}}{3}+\frac{5159}{6}}{\pi r^{2}}$$

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

$$h=\frac{-\frac{2\pi r^{3}}{3}+\frac{5159}{6}}{\pi r^{2}}$$

Divide \frac{5159}{6}-\frac{2\pi r^{3}}{3} by \pi r^{2}.

$$h=-\frac{2r}{3}+\frac{5159}{6\pi r^{2}}$$