Answer: [tex]4\ inches[/tex]
Step-by-step explanation:
The volume of a cube can be calculated with this formula:
[tex]V=s^3[/tex]
Where "s" is the length of any edge of the cube.
We know that the length of each side of any of the cubes that Mark uses to fill the container, is 1 inch. Then, we can find the volume of any of them:
[tex]V_{(cube})=(1\ in)^3\\\\V_{(cube})=1\ in^3[/tex]
Since Mark's container has the shape of a cube and he uses 64 of those cubes to completely fill this container, we get that the the volume of the container is:
[tex]V_{(container})=(64)(1\ in^3)\\\\V_{(container})=64\ in^3[/tex]
Finally, we can substitute this volume into the formula [tex]V=s^3[/tex] and the solve for "s":
[tex]64\ in^3=s^3\\\\s=\sqrt[3]{64\ in^3} \\\\s=4\ in[/tex]
