Question

a circle has center o, and points a and b lie on the circle. the measure of arc ab is 45° and the length of arc ab is 3 inches. what is the circumference, in inches, of the circle?
a 3
b 6
c 9
d 24

Explanation:

Step1: Use the arc - length formula

The formula for the length of an arc \(l\) is \(l=\frac{\theta}{360^{\circ}}\times C\), where \(\theta\) is the central angle of the arc and \(C\) is the circumference of the circle. We know that \(\theta = 45^{\circ}\) and \(l = 3\) inches. So, \(3=\frac{45^{\circ}}{360^{\circ}}\times C\).

Step2: Solve for \(C\)

First, simplify \(\frac{45^{\circ}}{360^{\circ}}=\frac{1}{8}\). Then the equation becomes \(3=\frac{1}{8}\times C\). Multiply both sides of the equation by \(8\) to isolate \(C\). So, \(C=3\times8\).

Answer:

\(24\) inches, so the answer is D.