Question

points c and d lie on a circle with radius 2 and arc $overparen{cd}$ has length $\frac{pi}{2}$. what fraction of the circumference of the circle is the length of arc $overparen{cd}$? a) $\frac{1}{8}$ b) $\frac{1}{4}$ c) $\frac{3}{8}$ d) $\frac{3}{4}$

Explanation:

Step1: Recall the circumference formula

The formula for the circumference of a circle is $C = 2\pi r$. Given $r = 2$, then $C=2\pi\times2 = 4\pi$.

Step2: Calculate the fraction

We want to find the fraction of the circumference that arc $\widehat{CD}$ represents. The length of arc $\widehat{CD}$ is $\frac{\pi}{2}$. The fraction is $\frac{\text{Length of arc }\widehat{CD}}{\text{Circumference}}=\frac{\frac{\pi}{2}}{4\pi}$.
Simplify the fraction: $\frac{\frac{\pi}{2}}{4\pi}=\frac{\pi}{2}\times\frac{1}{4\pi}=\frac{1}{8}$.

Answer:

A. $\frac{1}{8}$