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}
$