Answer:
[tex]\displaystyle h = \frac{A-2\pi r^2}{2\pi r}[/tex]
Step-by-step explanation:
Recall that the surface area A for a cylinder is given by:
[tex]\displaystyle A=2\pi r^2+2\pi rh[/tex]
And we want to solve for the height h.
First, subtract [tex]2\pi r^2[/tex] from both sides. This yields:
[tex]2\pi rh= A-2\pi r^2[/tex]
Now, we can dvide both sides by [tex]2\pi r[/tex]. This yields:
[tex]\displaystyle h = \frac{A-2\pi r^2}{2\pi r}[/tex]
And we're done!
