We are given the equation:

$v = \frac{1}{3} \pi r^2 (h - 1)$

We need to solve for $h$. To do this, follow these steps:

Step 1: Isolate the term involving $h$

Multiply both sides by 3 to eliminate the fraction:

$3v = \pi r^2 (h - 1)$

Step 2: Divide by $\pi r^2$

Now, divide both sides by $\pi r^2$:

$\frac{3v}{\pi r^2} = h - 1$

Step 3: Solve for $h$

Add 1 to both sides:

$h = \frac{3v}{\pi r^2} + 1$

Thus, the solution for $h$ is:

$h = \frac{3v}{\pi r^2} + 1$

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How does the formula change if the coefficient $\frac{1}{3}$ was different?
2. What happens to the value of $h$ if the radius $r$ increases?
3. How would you solve for $v$ in terms of $h$?
4. How does the equation change if the expression inside the parentheses was $(h - 2)$ instead of $(h - 1)$?
5. What real-world applications might involve using this type of equation?

Tip: Always check if you can simplify the equation early on to avoid complex calculations later.