For this case we have the following equation:
[tex]T = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]
We must solve the equation for the variable "h":
We subtract [tex]2 \pi * r ^ 2[/tex] from both sides of the equation:
[tex]T-2 \pi * r ^ 2 = 2 \pi * r * h[/tex]
We divide by [tex]2 \pi * r[/tex] on both sides of the equation:
[tex]\frac {T-2 \pi * r ^ 2} {2 \pi * r} = h\\h = \frac {T} {2 \pi * r} - \frac {2 \pi * r ^ 2} {2 \pi * r}\\h = \frac {T} {2 \pi * r} -r[/tex]
Answer:
[tex]h = \frac {T} {2 \pi * r} -r[/tex]
