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 $r=\frac{c}{2pi}$. find the radius of a circle that has a circumference of $16pi$.

Explanation:

Step1: Substitute the value of \(C\) into the formula

Given \(r=\frac{C}{2\pi}\) and \(C = 16\pi\), substitute \(C\) into the formula: \(r=\frac{16\pi}{2\pi}\).

Step2: Simplify the expression

Cancel out \(\pi\) in the numerator and denominator: \(\frac{16\pi}{2\pi}=\frac{16}{2}\). Then \(16\div2 = 8\).

Answer:

\(r = 8\)