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 ). ( r = 4 ), ( r = 8 ), ( r = 12 ), ( r = 16 )

Explanation:

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

Given \(r = \frac{C}{2\pi}\) and \(C = 16\pi\), we substitute \(C\): \(r=\frac{16\pi}{2\pi}\)

Step2: Simplify the expression

Cancel out \(\pi\) in the numerator and denominator: \(r=\frac{16}{2}\)
Calculate \(\frac{16}{2}=8\)

Answer:

\(r = 8\) (the second option)