Question

a large cube has a volume of 1 cubic unit. a small cube has a volume of $\frac{1}{27}$ of a cubic unit. what is the difference between the edge length of the large cube and the edge length of the small cube? units

Explanation:

Step1: Find edge - length of large cube

The volume formula for a cube is $V = s^{3}$, where $s$ is the edge - length. For the large cube with $V = 1$ cubic unit, we solve the equation $s_{1}^{3}=1$. Taking the cube - root of both sides, we get $s_{1}=\sqrt[3]{1}=1$ unit.

Step2: Find edge - length of small cube

For the small cube with $V=\frac{1}{27}$ cubic unit, we solve the equation $s_{2}^{3}=\frac{1}{27}$. Taking the cube - root of both sides, $s_{2}=\sqrt[3]{\frac{1}{27}}=\frac{1}{3}$ unit.

Step3: Calculate the difference

The difference $\Delta s=s_{1}-s_{2}$. Substitute $s_{1} = 1$ and $s_{2}=\frac{1}{3}$ into the formula: $\Delta s=1-\frac{1}{3}=\frac{3 - 1}{3}=\frac{2}{3}$ unit.

Answer:

$\frac{2}{3}$