Question

in the diagram below, what is the approximate length of the minor - arc de? a. 11.8 cm b. 23.6 cm c. 47.1 cm d. 19.7 cm

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc of a circle is $s = r\theta$, where $s$ is the arc - length, $r$ is the radius of the circle, and $\theta$ is the central angle in radians. First, convert the angle from degrees to radians. Given $\theta = 90^{\circ}$, and since $180^{\circ}=\pi$ radians, then $90^{\circ}=\frac{\pi}{2}$ radians, and $r = 15$ cm.

Step2: Calculate the arc - length

Substitute $r = 15$ cm and $\theta=\frac{\pi}{2}$ into the arc - length formula $s=r\theta$. So $s=15\times\frac{\pi}{2}=\frac{15\pi}{2}\approx\frac{15\times 3.14}{2}=23.55\approx23.6$ cm.

Answer:

B. 23.6 cm