Answer:
[tex]\boxed{ \frac{ 5}{ 9}}\\[/tex]
Step-by-step explanation:
Data:
V₁ = 125 in³
V₂ = 729 in³
Calculations:
A scale factor (C) is the ratio of corresponding side lengths (l) of the two prisms.
[tex]C=\frac{ l_{1}}{ l_{2}}\\[/tex]
The volume ratio is the cube of the scale factor.
[tex]\frac{V_{1}}{ V_{2}} = C^{3}\\[/tex]
[tex]\frac{125}{ 729} = C^{3}\\[/tex]
[tex]C = \sqrt [3]{\frac{ 125}{729 }} = \frac{5 }{9 }\\[/tex]
[tex]\boxed{ \textbf{The scale factor is } \frac{ 5}{ 9}.}\\[/tex]
