if the volume of a cube-shaped box is 729 cubic inches, which equation would you use to determine how many 1-inch cubes could fit along one side?

To determine how many 1-inch cubes could fit along one side of a cube-shaped box with a volume of 729 cubic inches, you can use the following equation:

Step-by-step explanation:

1. Volume of a cube formula:

V=s3V=s^3V=s3

where VVV is the volume and sss is the length of one side of the cube.

2. Given volume:

V=729 cubic inchesV=729\text{ cubic inches}V=729 cubic inches

3. Find the side length sss:

s3=729s^3=729s3=729

4. Solve for sss:

s=729s=\sqrt{729}s=729​

Since 9×9×9=7299\times 9\times 9=7299×9×9=729, we have:

s=9 inchess=9\text{ inches}s=9 inches

Final equation to determine the number of 1-inch cubes along one side:

s=729s=\sqrt{729}s=729​

This equation gives the number of 1-inch cubes that fit along one side of the box. In this case, 9 cubes fit along each side.