The formula for circumference is 𝐶=2𝜋𝑟C=2πr. Solve the formula for the variable r.

1. Break Down the Problem

We need to solve the formula for circumference $C$ in terms of the radius $r$. The formula given is: $C = 2\pi r$

2. Relevant Concepts

In this formula, $C$ is the circumference, $\pi$ is a mathematical constant (approximately 3.14159), and $r$ is the radius. To isolate $r$, we will rearrange the equation.

3. Analysis and Detail

To solve for $r$:

1. Start with the original equation: $C = 2\pi r$
2. Divide both sides of the equation by $2\pi$ to isolate $r$: $r = \frac{C}{2\pi}$

4. Verify and Summarize

The rearrangement is correct as we have isolated $r$ successfully through algebraic manipulation. The final formula for the radius $r$ in terms of the circumference $C$ is: $r = \frac{C}{2\pi}$

Final Answer

The solution for the variable $r$ is: $r = \frac{C}{2\pi}$