The given equation for the area of a cylinder is:
S = 2πr² + 2лrh
Subtract 2πr² from both sides
S - 2πr² = 2πr² - 2πr² + 2лrh
S - 2πr² = 2лrh
Divide both sides 2лr
[tex]\begin{gathered} \frac{S-2\pi r^2}{2\pi r}=\frac{2\pi rh}{2\pi r} \\ \\ h=\frac{S-2\pi r^{2}}{2\pi r} \end{gathered}[/tex]