The problem asks to write an equation that would allow us to easily find the height $h$ of a cylinder, given the volume equation for a cylinder:

$V = \pi r^2 h$

where:

• $V$ is the volume of the cylinder,
• $r$ is the radius of the cylinder,
• $h$ is the height of the cylinder.

To solve for the height $h$, we can rearrange the equation by isolating $h$ on one side:

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

This equation allows us to calculate the height of the cylinder if we know the volume $V$ and the radius $r$.

Would you like further details or have any questions about this process?

Here are 5 related questions:

1. How do you calculate the volume of a cylinder if both height and radius are given?
2. What happens to the height if the volume increases but the radius stays the same?
3. Can the formula for the volume of a cylinder be applied to a cone? Why or why not?
4. How would you calculate the radius of a cylinder if you only know the volume and height?
5. What is the physical interpretation of $\pi r^2$ in the volume formula?

Tip: Always double-check your units when solving for volume, height, or radius to ensure they are consistent.