Remember that whenever a figure is scaled by a factor k, then its area gets scaled by a factor of k^2 and its volume gets scaled by a factor of k^3. If the area factor for a cylinder is 19.16, then the scale factor is related to it by the following expression:

Then:
![\begin{gathered} k=\sqrt[]{19.16} \\ \Rightarrow k=4.377213726\ldots \\ \therefore k\approx4.38 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/emtje6kgvc0aq39n0h2ujlt15i3ez46bei.png)
Up to two decimal places, the scale factor is 4.38