What happens to the volume of a shape when the scale factor of enlargement is n?

When a shape undergoes enlargement with a scale factor of ( n ), every linear dimension of the shape, such as length, width, and height, is multiplied by ( n ).

Volume is a three-dimensional measure, and it can be understood as the product of the length, width, and height of an object. Therefore, if each linear measurement is multiplied by ( n ), the new dimensions of the shape become ( n \times \text{length} ), ( n \times \text{width} ), and ( n \times \text{height} ).

The volume of the original shape can be expressed as:

[ \text{Volume} = \text{length} \times \text{width} \times \text{height} ]

For the enlarged shape, the new volume becomes:

[ \text{New Volume} = (n \times \text{length}) \times (n \times \text{width}) \times (n \times \text{height}) = n^3 \times (\text{length} \times \text{width} \times \text{height}) ]

This shows that the new volume is ( n^3 )