Question

the formula for the circumference of a circle is $c = 2pi r$, where $r$ is the radius and $c$ is the circumference. the equation solved for $r$ is $r = \frac{c}{2\pi}$. find the radius of a circle that has a circumference of $16\pi$. $r = 8$ $r = 16$ $r = 4$ $r = 12$

Explanation:

Step1: Identify given values

We know the circumference formula solved for \( r \) is \( r=\frac{C}{2\pi} \), and the circumference \( C = 16\pi \).

Step2: Substitute \( C \) into the formula

Substitute \( C = 16\pi \) into \( r=\frac{C}{2\pi} \), we get \( r=\frac{16\pi}{2\pi} \).

Step3: Simplify the expression

Simplify \( \frac{16\pi}{2\pi} \), the \( \pi \) terms cancel out, and \( \frac{16}{2}=8 \), so \( r = 8 \).

Answer:

\( r = 8 \) (corresponding to the option with \( r = 8 \))