Question

the volume of a cube is 512 cubic inches. what is the length of each side of the cube?

Explanation:

Step1: Recall cube volume formula

The volume $V$ of a cube with side length $s$ is $V = s^3$.

Step2: Substitute given volume

We know $V = 512$, so $s^3 = 512$.

Step3: Solve for side length

Find the cube root of 512: $s = \sqrt[3]{512}$
Since $8 \times 8 \times 8 = 512$, $\sqrt[3]{512} = 8$.

Answer:

8 inches