Question

a circle has an arc of length 8 with central angle 6°. find the circumference of the circle.

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) is \(s=\frac{\theta}{360^{\circ}}\times C\), where \(\theta\) is the central angle and \(C\) is the circumference.

Step2: Substitute the given values into the formula

We know that \(s = 8\) and \(\theta=6^{\circ}\). Substituting into \(s=\frac{\theta}{360^{\circ}}\times C\), we get \(8=\frac{6^{\circ}}{360^{\circ}}\times C\).

Step3: Solve for \(C\)

First, simplify \(\frac{6^{\circ}}{360^{\circ}}=\frac{1}{60}\). Then the equation becomes \(8=\frac{1}{60}\times C\).
Multiply both sides of the equation by \(60\): \(C = 8\times60=480\).

Answer:

$480$