solve for the indicated variable
v=1/3pi r squared (h-1);h

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.

solve for the indicated variable v=1/3pi r squared (h-1);h

Learn how to solve for the height (h) in the equation v = (1/3)πr^2(h - 1) with a step-by-step solution. This guide covers algebraic concepts such as isolating variables and manipulating equations. Suitable for high school students in Grades 9-12.

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