Question

question 7 of 10
in the diagram below, what is the approximate length of the minor arc $widehat{ab}$?
a. 6.3 cm
b. 5.2 cm
c. 3.1 cm
d. 7.9 cm

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ of a circle is $s = r\theta$ (where $r$ is the radius and $\theta$ is the central - angle in radians). First, convert the angle from degrees to radians. We know that to convert degrees to radians, we use the conversion factor $\theta_{rad}=\frac{\pi}{180}\times\theta_{deg}$. Given $\theta_{deg}=72^{\circ}$, then $\theta_{rad}=\frac{\pi}{180}\times72=\frac{2\pi}{5}$ radians.

Step2: Identify the radius

The radius of the circle $r = 5$ cm.

Step3: Calculate the arc - length

Substitute $r = 5$ cm and $\theta=\frac{2\pi}{5}$ into the arc - length formula $s=r\theta$. So $s = 5\times\frac{2\pi}{5}=2\pi\approx2\times3.14 = 6.28\approx6.3$ cm.

Answer:

A. 6.3 cm