Which term describes the relationship between the original volume and the enlarged volume when the scale factor is n?

When a three-dimensional object is enlarged using a scale factor of n, the relationship between the original volume and the enlarged volume is determined by cubing the scale factor. This is because volume is a measure of three-dimensional space, which means you multiply the scaling effects in each of the three dimensions (length, width, and height).

If you consider the original dimensions of an object as x, y, and z, when scaled by a factor of n, the new dimensions become nx, ny, and nz. The original volume can be expressed as V = x * y * z, while the enlarged volume would be V' = (nx) * (ny) * (nz) = n³ * x * y * z. Therefore, the relationship between the original volume and the enlarged volume reveals that the enlarged volume is n³ times larger than the original volume.

This demonstrates why the correct answer is that the enlarged volume is increased by n³, reflecting the three-dimensional nature of volume scaling.