The formula for the volume $V$ of a right circular cylinder is:

$V = \pi r^2 h$

We are told that the height $h$ is three times the radius $r$. This gives us the relationship:

$h = 3r$

Substituting $h = 3r$ into the volume formula:

$V = \pi r^2 (3r) = 3\pi r^3$

Thus, the volume $V$ as a function of $r$ is:

$V(r) = 3\pi r^3$

Let me know if you'd like any further explanation!

Here are some related questions to explore:

1. What is the volume of the cylinder when $r = 2$ units?
2. How does the volume change if the height is doubled?
3. Can you express the surface area of the same cylinder as a function of $r$?
4. What happens to the volume if the radius is halved?
5. How does the volume formula differ for a cone?

Tip: When the height is proportional to the radius, simplifying the volume formula early helps save time!