Once you have the formula, plug in $r = 3$ and $V = 108\pi$. You should get an equation with only one unknown, $h$.

After substituting, simplify $3^2$ and then look for common factors on both sides (especially involving $\pi$) to make solving for $h$ easier.

In Desmos, type the expression 108*pi/(pi*3^2) to represent $h = \frac{108\pi}{\pi \cdot 3^2}$. The numerical value that Desmos outputs is the height of the cylinder in meters.

The volume $V$ of a right circular cylinder with radius $r$ and height $h$ is given by

We are given $V$ and $r$ and need to solve for $h$.

The problem states that the radius is $3$ meters and the volume is $108\pi$ cubic meters.

Substitute $V = 108\pi$ and $r = 3$ into the formula:

Compute $3^2 = 9$:

First, notice that $\pi$ appears on both sides of the equation, so you can divide both sides by $\pi$ to cancel it:

Now solve for $h$ by dividing both sides by $9$:

So, the height of the cylinder is 12 meters.