Formula for surface area of cylinder is:
[tex]S=2\pi r^2+2\pi rh[/tex]We need to solve for h.
We take the term with h to one side and everything else to another, and solve:
[tex]\begin{gathered} S=2\pi r^2+2\pi rh \\ 2\pi rh=S-2\pi r^2 \\ h=\frac{S-2\pi r^2}{2\pi r} \end{gathered}[/tex]Another simplified version:
[tex]\begin{gathered} h=\frac{S-2\pi r^2}{2\pi r} \\ h=\frac{S}{2\pi r}-\frac{2\pi r^2^{}}{2\pi r} \\ h=\frac{S}{2\pi r}-r \end{gathered}[/tex]