The formula given for the volume $V$ of a cone is:

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

where:

• $V$ is the volume,
• $r$ is the radius of the base,
• $h$ is the height,
• $\pi$ is the constant Pi (approximately 3.14159).

You are asked to solve for the height $h$ in terms of $V$, $r$, and $\pi$.

To isolate $h$, follow these steps:

1. Start with the formula for the volume of the cone: $V = \frac{1}{3} \pi r^2 h$
2. Multiply both sides of the equation by 3 to eliminate the fraction: $3V = \pi r^2 h$
3. Divide both sides by $\pi r^2$ to solve for $h$: $h = \frac{3V}{\pi r^2}$

Thus, the formula for the height $h$ is:

$h = \frac{3V}{\pi r^2}$

Would you like more details or clarifications?

Here are 5 related questions to expand your understanding:

1. How does the volume change if the radius is doubled but the height remains the same?
2. Can you derive the volume formula for other 3D shapes like cylinders or spheres?
3. How would you calculate the volume if only the slant height and radius were given?
4. What happens to the volume if both the height and radius of the cone are halved?
5. How would you compute the volume of a frustum (a truncated cone)?

Tip: When manipulating formulas, always perform the same operation on both sides of the equation to maintain equality.