To determine the side length of a cube when its volume is given, we need to use the formula for the volume of a cube:
[tex]\[ V = s^3 \][/tex]
where [tex]\( V \)[/tex] is the volume and [tex]\( s \)[/tex] is the side length. Given that the volume [tex]\( V \)[/tex] is 6859 mm³, we need to solve for [tex]\( s \)[/tex].
Here are the detailed steps:
1. Start with the volume formula:
[tex]\[ V = s^3 \][/tex]
2. Plug in the given volume:
[tex]\[ 6859 = s^3 \][/tex]
3. To find the side length [tex]\( s \)[/tex], take the cube root of both sides of the equation.
[tex]\[ s = \sqrt[3]{6859} \][/tex]
When you calculate the cube root of 6859, you get:
[tex]\[ s = 18.999999999999996 \][/tex]
This value is very close to 19. Given the context, it's reasonable to state that the side length of the cube is:
[tex]\[ s \approx 19 \, \text{mm} \][/tex]
Thus, the side length of the cube is approximately 19 mm.
