Step 1: Use conservation of volume.
When metal is melted and recast, no material is lost, so the volume stays the same. The volume of a cylinder is $V = \pi r^2 h$.
Step 2: Write the original volume.
The first cylinder has radius $r$ and height $h$, so its volume is $V_1 = \pi r^2 h$.
Step 3: Apply the change in radius.
The radius is reduced, and the height adjusts so that the same metal is reused. Whatever the new radius is, the height changes to keep the product $\pi (\text{radius})^2 (\text{height})$ unchanged.
Step 4: Compare the two volumes.
Since the recast cylinder is made from the very same metal with nothing added or removed, its volume $V_2$ must equal $V_1$.
Step 5: Form the ratio.
\[ \frac{V_1}{V_2} = \frac{\pi r^2 h}{\pi r^2 h} = 1 \] The melting and recasting cannot change the total volume.
Step 6: State the ratio.
So the ratio of the volumes is $1$ to $1$. Therefore \[ \boxed{1:1} \]