Mathematics

The core concept here is interpreting mathematical solutions in a real-world context. When you solve an equation, you get all mathematical solutions—but not all of them make physical sense. Since $r$ represents a radius, it must be a positive length; a radius of zero would mean no pond exists at all. This is why you need to check your answers against the constraints of the problem, not just the algebra.

The core concept here is interpreting mathematical solutions in a real-world context. When you solve an equation, you get all mathematical solutions—but not all of them make physical sense. Since $r$ represents a radius, it must be a positive length; a radius of zero would mean no pond exists at all. This is why you need to check your answers against the constraints of the problem, not just the algebra.