The volume of a cube is given by the formula:

$V = s^3$

where $s$ is the length of a side of the cube.

Step 1: Simplify the volume

The given volume is:

$V = \frac{729}{27} \text{ cubic inches.}$

Simplify the fraction:

$\frac{729}{27} = 27.$

Thus, the volume of the cube is 27 cubic inches.

Step 2: Solve for the side length

We know:

$s^3 = 27.$

Take the cube root of both sides:

$s = \sqrt[3]{27}.$

Since $27 = 3^3$, we find:

$s = 3 \text{ inches.}$

Final Answer:

The length of a side of the cube is 3 inches.

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Would you like me to explain this further or expand on related concepts? Here are 5 related questions for practice:

1. What is the volume of a cube with a side length of 4 inches?
2. If the surface area of a cube is 54 square inches, what is the side length of the cube?
3. How do you calculate the volume of a rectangular prism?
4. If the volume of a cube is halved, how does the side length change?
5. What is the side length of a cube with a volume of 64 cubic inches?

Tip:

Remember that the cube root of a number is the value that, when multiplied by itself three times, equals the original number.