The relationship between the two cylinders involves the volume factor
[tex]\begin{gathered} \text{volume factor=(scale factor)}^3 \\ \text{therefore, } \\ \text{scale factor=}\sqrt[3]{volume\text{ factor}} \end{gathered}[/tex][tex]\begin{gathered} \text{volume factor=}\frac{smaller\text{ volume}}{larger\text{ volume}} \\ \text{volume factor=}\frac{27\operatorname{cm}^3}{1331\operatorname{cm}}^{} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{scale factor=}\sqrt[3]{\frac{27\operatorname{cm}}{1331\operatorname{cm}^3}} \\ \text{Scale factor}=\frac{3}{11} \\ \text{Therefore , the scale factor} \\ =3\colon11 \end{gathered}[/tex]Hence ,
The scale factor = 3:11
