Question

a cube - shaped box has a volume of $\frac{1}{8}$ of a cubic meter. what is the perimeter of each of its faces? meters

Explanation:

Step1: Find the side - length of the cube

The volume formula of a cube is $V = s^{3}$, where $V$ is the volume and $s$ is the side - length. Given $V=\frac{1}{8}\text{ m}^3$, we solve the equation $\frac{1}{8}=s^{3}$ for $s$. Taking the cube - root of both sides, $s=\sqrt[3]{\frac{1}{8}}=\frac{1}{2}$ m.

Step2: Calculate the perimeter of a face

Each face of a cube is a square. The perimeter formula of a square is $P = 4s$. Substituting $s = \frac{1}{2}$ m into the formula, we get $P=4\times\frac{1}{2}=2$ m.

Answer:

2