The problem is to solve the formula for the volume of a cube [tex]\(V = s^3\)[/tex] for the side length [tex]\(s\)[/tex].
Let's start with the given formula:
[tex]\[ V = s^3 \][/tex]
We need to isolate [tex]\(s\)[/tex]. To do this, we will take the cube root of both sides of the equation:
[tex]\[ s = \sqrt[3]{V} \][/tex]
Alternatively, this can be expressed using exponent notation as:
[tex]\[ s = V^{1/3} \][/tex]
Thus, the correct solution for [tex]\(s\)[/tex] in terms of [tex]\(V\)[/tex] is:
[tex]\[ s = \sqrt[3]{V} \][/tex]
This shows that the side length [tex]\(s\)[/tex] is the cube root of the volume [tex]\(V\)[/tex].
Among the given choices:
- [tex]\( s = \sqrt{V} \)[/tex] is incorrect as it represents the square root, not the cube root.
- [tex]\( s = \frac{V}{3} \)[/tex] is incorrect as it divides the volume by 3, not related to the correct solution.
- [tex]\( s = \sqrt[3]{V} \)[/tex] is correct, as it represents the cube root of the volume.
- [tex]\( s = V^3 \)[/tex] is incorrect as it represents the volume raised to the power of 3, not taking the cube root.
Therefore, the correct choice is:
[tex]\[ s = \sqrt[3]{V} \][/tex]
