To solve the equation \( s = \pi rh + \pi r^2 \) for \( h \), follow these steps:

1. Start with the given equation:
   \[
   s = \pi rh + \pi r^2
   \]

2. Isolate the term involving \( h \) on one side of the equation:
   \[
   s - \pi r^2 = \pi rh
   \]

3. Solve for \( h \) by dividing both sides of the equation by \( \pi r \):
   \[
   h = \frac{s - \pi r^2}{\pi r}
   \]

So, the solution for \( h \) is:
\[
h = \frac{s - \pi r^2}{\pi r}
\]

Would you like further details or have any questions?

Here are 5 related questions:

1. How would the solution change if \( r \) were to be solved instead of \( h \)?
2. What is the value of \( h \) if \( s = 50 \), \( r = 3 \), and \( \pi \) is approximated as 3.14?
3. How does this equation relate to the surface area of a cylinder?
4. Can you rewrite the equation for \( s \) in terms of \( r \) and \( h \) alone?
5. What happens to \( h \) as \( r \) approaches 0?

**Tip:** When solving for a variable, always check if there is a common factor you can factor out to simplify the equation.

Learn how to solve the equation s = πrh + πr^2 for h with a step-by-step solution. This problem involves algebraic manipulation and equation solving. Suitable for high school students.

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