For this case, we have that by definition, the surface area of a cylinder, is given by:
[tex]A = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]
Where:
A: It is the area of the surface
h: It is the height of the cylinder
r: It's the radio
If you want to find the height as a function of "A", we clear:
Subtracting[tex]2 \pi * r ^ 2[/tex] on both sides of the equation:
[tex]A-2 \pi * r ^ 2 = 2 \pi * r * h[/tex]
Dividing both sides of the equation between [tex]2 \pi * r[/tex]:
[tex]\frac {A-2 \pi * r ^ 2} {2 \pi * r} = h[/tex]
So, we have "h" as a function of "A"
Answer:
[tex]h = \frac {A-2 \pi * r ^ 2} {2 \pi * r}[/tex]
