from m$^3$ to length, width, height of cube

Question

Is it possible to calculate the length, width, height of a cube, based on just the m$^3$.

For example if I have a cube with sides of $5$ meters: the m$^3$ is $125$ m$^3$.

Is it possible to go back from $125$ m$^3$ to the sizes of the $3$ dimensions (for a cube (equal dimensions)).

Answer 1

Yes. If the side of the cube is $a$, and you know the volume of the cube is $V$, then you know that $a$ is the solution to the equation $$a^3=V,$$

meaning that $a=\sqrt[3]{V}$.