Question

if a cube has a volume of $\frac{1}{8}$ cubic units, what is the area of one of its faces? square units

Explanation:

Step1: Find the side - length of the cube

Let the side - length of the cube be $a$. The volume formula of a cube is $V = a^{3}$. Given $V=\frac{1}{8}$, then $a^{3}=\frac{1}{8}$, so $a=\sqrt[3]{\frac{1}{8}}=\frac{1}{2}$.

Step2: Calculate the area of one face

The area formula of one face of a cube is $A = a^{2}$. Substitute $a = \frac{1}{2}$ into the formula, we get $A=(\frac{1}{2})^{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$