1. Let's clarify the context: typically, when you see a change from $r^2$ to $r^3$, it involves a formula where volume or a three-dimensional measure is considered instead of area or a two-dimensional measure. 2. For example, the surface area of a sphere is proportional to $r^2$, while the volume of a sphere is proportional to $r^3$. 3. The reason for changing from $r^2$ to $r^3$ is because volume depends on three dimensions (length, width, height), so the radius is cubed. 4. In step 6, if the problem involves volume or a quantity that depends on the cube of the radius, we must use $r^3$ instead of $r^2$ to correctly represent the relationship. 5. This is based on the geometric rule that volume scales with the cube of the linear dimension, while area scales with the square. 6. So, changing $r^2$ to $r^3$ is necessary to correctly calculate or represent volume or any 3D property related to the radius. Final answer: We change $r^2$ to $r^3$ because the problem requires considering volume or a three-dimensional measure, which depends on the cube of the radius, not the square.