Answer: If that change is made, the new volume will be [tex]3,375\ mm^3[/tex]
Step-by-step explanation:
For this exercise it is important to remember that the formula used to calculate the volume of a cube is the following:
[tex]V=s^3[/tex]
Where "s" is the lenght of any edge of the cube.
You know that the current days have edge length of 5 mm.
Then, knowing the formula for calculate the volume of a cube, you get that the current volume of any of those cubes made by the company is:
[tex]V_1=(5\ mm)^3\\\\V_1=125\ mm^3[/tex]
Since they want to increase the length to 15 mm, you can identify that:
[tex]s=15\ mm[/tex]
Therefore, knowing this new edge you can calculate the new volume.
You get that this is:
[tex]V_2=(15\ mm)^3\\\\V_2=3,375\ mm^3[/tex]
