Intermediate Algebra, Chapter 2, 2.2, Section 2.2, Problem 10

Solve $\displaystyle S = 2 \pi rh + 2 \pi r^2$ for $h$.


$\begin{equation} \begin{aligned} S =& 2 \pi rh + 2 \pi r^2 && \text{Given equation} \\ S - 2 \pi r^2 =& 2 \pi rh + 2 \pi r^2 - 2 \pi r^2 && \text{Subtract each side by $2 \pi r^2$} \\ S - 2 \pi r^2 =& 2 \pi rh && \text{Combine like terms} \\ S - 2 \pi r^2 =& (2 \pi r)h && \text{Associative property} \\ \frac{S - 2 \pi r^2}{2 \pi r} =& \frac{(2 \pi r)}{2 \pi r} && \text{Divide each side by $2 \pi r$} \\ h =& \frac{S - 2 \pi r^2}{2 \pi r} && \text{Solve for $h$} \end{aligned} \end{equation}$