https://file.aiquickdraw.com/mathbot/file/1727226380834pqovf32t.jpg

The equation provided in the image is:

\[
V = \frac{1}{3} \pi r^2 (h - l)
\]

You are asked to "get *h* alone", meaning we need to solve the equation for *h*. Let's work through it step by step.

### Step 1: Start with the given equation
\[
V = \frac{1}{3} \pi r^2 (h - l)
\]

### Step 2: Eliminate the fraction
Multiply both sides of the equation by 3 to remove the fraction:
\[
3V = \pi r^2 (h - l)
\]

### Step 3: Isolate the term involving *h*
Divide both sides by \(\pi r^2\):
\[
\frac{3V}{\pi r^2} = h - l
\]

### Step 4: Solve for *h*
Add *l* to both sides to isolate *h*:
\[
h = \frac{3V}{\pi r^2} + l
\]

Thus, the equation solved for *h* is:
\[
h = \frac{3V}{\pi r^2} + l
\]

Would you like more details, or do you have any questions?

Here are five related questions:
1. What does the variable *V* represent in this context?
2. How does the radius *r* affect the height *h* in this formula?
3. Can this formula be applied to calculate the height of a cone given its volume?
4. What units would typically be used for each variable in this formula?
5. How would the equation change if the cone had a slant height instead of a vertical height?

**Tip:** Always check the dimensions or units of each variable to ensure consistency when solving physics or geometry problems.

Solve the equation V = 1/3 π r^2 (h - l) for h.

Learn how to solve for the height 'h' in the equation V = 1/3 π r^2 (h - l). This problem covers essential algebraic and geometric concepts, suitable for students in Grades 9-11.

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