Given a circle with a circumference of $16$, what is the radius $r$ of the circle?

• A. $r=4$
• B. $r=12$
• C. $r=8$
• D. $r=16$

Answer: (A)

Verified step by step guidance

1. Recall the formula for the circumference of a circle: \(C = 2 \\pi r\), where \(C\) is the circumference and \(r\) is the radius.
2. Substitute the given circumference value into the formula: \(16 = 2 \\pi r\).
3. To isolate \(r\), divide both sides of the equation by \(2 \\pi\): \(r = \frac{16}{2 \\pi}\).
4. Simplify the fraction: \(r = \frac{16}{2 \\pi} = \frac{8}{\\pi}\).
5. Interpret the result: the radius \(r\) is \(\frac{8}{\\pi}\) units. If you need a numerical approximation, you can calculate this value using \(\\pi \approx 3.14\).