To determine the side length [tex]\( s \)[/tex] of a cube with a volume of [tex]\( 64 \, \text{mm}^3 \)[/tex], we follow the steps:
1. Understand the formula for the volume of a cube:
The volume [tex]\( V \)[/tex] of a cube is given by the formula:
[tex]\[
V = s^3
\][/tex]
where [tex]\( s \)[/tex] is the side length of the cube.
2. Substitute the given volume into the formula:
Given that the volume [tex]\( V \)[/tex] is [tex]\( 64 \, \text{mm}^3 \)[/tex], we substitute this value into the formula:
[tex]\[
64 = s^3
\][/tex]
3. Solve for the side length [tex]\( s \)[/tex]:
To find [tex]\( s \)[/tex], we need to undo the cube by taking the cube root of both sides of the equation. So, we apply the cube root:
[tex]\[
\sqrt[3]{64} = \sqrt[3]{s^3}
\][/tex]
4. Simplify the expression:
The cube root of [tex]\( s^3 \)[/tex] is simply [tex]\( s \)[/tex], and the cube root of [tex]\( 64 \)[/tex] is approximately [tex]\( 3.9999999999999996 \)[/tex]. Therefore, we have:
[tex]\[
s = 3.9999999999999996 \, \text{mm}
\][/tex]
So, the side length of the cube is [tex]\( 3.9999999999999996 \, \text{mm} \)[/tex].
