The volume of a cube is $166.375{\text{cm}}^3$. Find its side (in $\text{cm}$).

The volume of a cube with side $a$ is given by:
$$V=a^3$$
Given $V=166.375{\text{cm}}^3$:
$$a^3=166.375=\frac{166375}{1000}$$
Taking the cube root on both sides:
$$a=\frac{\sqrt[3]{166375}}{\sqrt[3]{1000}}$$
Since $55^3=166375$:
$$a=\frac{55}{10}=5.5\text{cm}$$