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For question 5, you are asked to solve the equation \( S = 2\pi rh + 2\pi r^2 \) for \( h \).

### Step-by-Step Solution:
1. **Start with the equation:**
   \[
   S = 2\pi rh + 2\pi r^2
   \]

2. **Subtract \( 2\pi r^2 \) from both sides to isolate the term involving \( h \):**
   \[
   S - 2\pi r^2 = 2\pi rh
   \]

3. **Now, divide both sides by \( 2\pi r \) to solve for \( h \):**
   \[
   h = \frac{S - 2\pi r^2}{2\pi r}
   \]

This matches the first option:
\[
h = \frac{S - 2\pi r^2}{2\pi r}
\]

So, the correct answer for question 5 is the **first option**.

---

For question 6, you are asked to solve the formula \( m = \frac{x_1 + x_2}{2} \) for \( x_1 \).

### Step-by-Step Solution:
1. **Start with the equation:**
   \[
   m = \frac{x_1 + x_2}{2}
   \]

2. **Multiply both sides by 2 to get rid of the denominator:**
   \[
   2m = x_1 + x_2
   \]

3. **Subtract \( x_2 \) from both sides to isolate \( x_1 \):**
   \[
   x_1 = 2m - x_2
   \]

This matches the third option:
\[
x_1 = 2m - x_2
\]

So, the correct answer for question 6 is the **third option**.

---

Would you like more details or clarifications on any step? Here are five related questions to deepen your understanding:

1. How can you isolate a variable when there are multiple terms involving the variable?
2. What are some common mistakes when solving equations with constants like \( \pi \)?
3. How do you solve for a variable in a fraction?
4. Can you generalize the process of solving for any variable in a linear equation?
5. Why is it important to perform the same operation on both sides of an equation?

**Tip:** Always check your final solution by plugging it back into the original equation to ensure it satisfies all terms.

Solve the following equation for h: S = 2πrh + 2πr^2

Learn how to solve the equation S = 2πrh + 2πr^2 for h. This problem covers key algebraic concepts such as isolating variables and working with equations involving constants like π. Suitable for students in Grades 9-12.

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