Answer: 6 in.
Step-by-step explanation:
Given
The volume of the small cube is [tex]V_1=27\ in.^3[/tex]
The volume of the large cube box is [tex]V_2=729\ in.^3[/tex]
The volume of a cube is [tex](a)^3[/tex]
[tex]\Rightarrow a_1^3=27\quad (a_1=\text{side length of small cube})\\\Rightarrow a_1=3\ in.\\\Rightarrow a_2^3=729\quad (a_2=\text{side length of large cube})\\\Rightarrow a_2=9\ in.[/tex]
The DIfference between the edge length is [tex]a_2-a_1=9-3=6\ in.[/tex]
