How does increasing the size of a cube affect its volume?

Increasing the size of a cube affects its volume in a specific mathematical way. The volume of a cube is calculated using the formula ( V = s^3 ), where ( s ) is the length of one side of the cube. When the size of the cube increases, the side length ( s ) increases as well.

If the side length is increased, the volume does not just increase linearly, but rather it increases exponentially because the volume is proportional to the cube of the side length. For instance, if you double the side length of the cube, the new volume becomes ( (2s)^3 = 8s^3 ), which is eight times the original volume. This demonstrates that even a small increase in the side length leads to a large increase in volume, illustrating the exponential growth of volume as the dimensions of the cube are increased.

This relationship emphasizes how sensitive a cube's volume is to changes in size and further confirms the exponential nature of this correlation.