To solve for $h$ from the surface area equation of a cylinder:

$A = 2\pi r^2 + 2\pi r h$

Step-by-step solution:

1. Subtract $2\pi r^2$ from both sides to isolate the term with $h$: $A - 2\pi r^2 = 2\pi r h$

2. Divide both sides by $2\pi r$ to solve for $h$: $h = \frac{A - 2\pi r^2}{2\pi r}$

Thus, the formula for $h$ in terms of $A$ and $r$ is: $h = \frac{A - 2\pi r^2}{2\pi r}$

Let me know if you need further details or have any questions!

Here are 5 related questions:

1. What is the volume of a cylinder in terms of $r$ and $h$?
2. How does the surface area formula change if the cylinder is hollow?
3. If $A = 100 \, \text{cm}^2$ and $r = 2 \, \text{cm}$, what is the height $h$?
4. How would you modify the surface area formula for a cone instead of a cylinder?
5. How does increasing the radius affect the surface area for a fixed height?

Tip: Always pay attention to the units of measurement in problems involving surface area or volume!