Solution:
[tex]$h=\frac{ A-2\pi r^2}{2\pi r }[/tex]
Given data:
[tex]A=2\pi r^2+2\pi r h[/tex]
Let us determine what is h using given A.
[tex]A=2\pi r^2+2\pi r h[/tex]
Subtract [tex]2\pi r^2[/tex] on both sides of the expression.
⇒ [tex]A-2\pi r^2=2\pi r^2+2\pi r h-2\pi r^2[/tex]
⇒ [tex]A-2\pi r^2=2\pi r^2-2\pi r^2+2\pi r h[/tex]
⇒ [tex]A-2\pi r^2=2\pi r h[/tex]
Divide both sides of the expression by [tex]2\pi r[/tex].
[tex]$\frac{ A-2\pi r^2}{2\pi r }=\frac{2\pi rh }{2\pi r }[/tex]
[tex]$\frac{ A-2\pi r^2}{2\pi r }=h[/tex]
[tex]$h=\frac{ A-2\pi r^2}{2\pi r }[/tex]
Option C is the correct answer.
Hence [tex]$h=\frac{ A-2\pi r^2}{2\pi r }[/tex].
